number_theory.von_mangoldt | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

c946d609

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

61b5e275

bump to nightly-2024-02-12-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

56ad230b

Diff

@@ -44,23 +44,23 @@ open Finset
 
 open scoped ArithmeticFunction
 
-#print Nat.ArithmeticFunction.log /-
+#print ArithmeticFunction.log /-
 /-- `log` as an arithmetic function `ℕ → ℝ`. Note this is in the `nat.arithmetic_function`
 namespace to indicate that it is bundled as an `arithmetic_function` rather than being the usual
 real logarithm. -/
-noncomputable def log : ArithmeticFunction ℝ :=
+noncomputable def ArithmeticFunction.log : ArithmeticFunction ℝ :=
   ⟨fun n => Real.log n, by simp⟩
-#align nat.arithmetic_function.log Nat.ArithmeticFunction.log
+#align nat.arithmetic_function.log ArithmeticFunction.log
 -/
 
-#print Nat.ArithmeticFunction.log_apply /-
+#print ArithmeticFunction.log_apply /-
 @[simp]
-theorem log_apply {n : ℕ} : log n = Real.log n :=
+theorem ArithmeticFunction.log_apply {n : ℕ} : ArithmeticFunction.log n = Real.log n :=
   rfl
-#align nat.arithmetic_function.log_apply Nat.ArithmeticFunction.log_apply
+#align nat.arithmetic_function.log_apply ArithmeticFunction.log_apply
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt /-
+#print ArithmeticFunction.vonMangoldt /-
 /--
 The `von_mangoldt` function is the function on natural numbers that returns `log p` if the input can
 be expressed as `p^k` for a prime `p`.
@@ -69,72 +69,74 @@ smallest prime factor.
 
 In the `arithmetic_function` locale, we have the notation `Λ` for this function.
 -/
-noncomputable def vonMangoldt : ArithmeticFunction ℝ :=
+noncomputable def ArithmeticFunction.vonMangoldt : ArithmeticFunction ℝ :=
   ⟨fun n => if IsPrimePow n then Real.log (minFac n) else 0, if_neg not_isPrimePow_zero⟩
-#align nat.arithmetic_function.von_mangoldt Nat.ArithmeticFunction.vonMangoldt
+#align nat.arithmetic_function.von_mangoldt ArithmeticFunction.vonMangoldt
 -/
 
-scoped[ArithmeticFunction] notation "Λ" => Nat.ArithmeticFunction.vonMangoldt
+scoped[ArithmeticFunction] notation "Λ" => ArithmeticFunction.vonMangoldt
 
-#print Nat.ArithmeticFunction.vonMangoldt_apply /-
-theorem vonMangoldt_apply {n : ℕ} : Λ n = if IsPrimePow n then Real.log (minFac n) else 0 :=
+#print ArithmeticFunction.vonMangoldt_apply /-
+theorem ArithmeticFunction.vonMangoldt_apply {n : ℕ} :
+    Λ n = if IsPrimePow n then Real.log (minFac n) else 0 :=
   rfl
-#align nat.arithmetic_function.von_mangoldt_apply Nat.ArithmeticFunction.vonMangoldt_apply
+#align nat.arithmetic_function.von_mangoldt_apply ArithmeticFunction.vonMangoldt_apply
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt_apply_one /-
+#print ArithmeticFunction.vonMangoldt_apply_one /-
 @[simp]
-theorem vonMangoldt_apply_one : Λ 1 = 0 := by simp [von_mangoldt_apply]
-#align nat.arithmetic_function.von_mangoldt_apply_one Nat.ArithmeticFunction.vonMangoldt_apply_one
+theorem ArithmeticFunction.vonMangoldt_apply_one : Λ 1 = 0 := by simp [von_mangoldt_apply]
+#align nat.arithmetic_function.von_mangoldt_apply_one ArithmeticFunction.vonMangoldt_apply_one
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt_nonneg /-
+#print ArithmeticFunction.vonMangoldt_nonneg /-
 @[simp]
-theorem vonMangoldt_nonneg {n : ℕ} : 0 ≤ Λ n :=
+theorem ArithmeticFunction.vonMangoldt_nonneg {n : ℕ} : 0 ≤ Λ n :=
   by
   rw [von_mangoldt_apply]
   split_ifs
   · exact Real.log_nonneg (one_le_cast.2 (Nat.minFac_pos n))
   rfl
-#align nat.arithmetic_function.von_mangoldt_nonneg Nat.ArithmeticFunction.vonMangoldt_nonneg
+#align nat.arithmetic_function.von_mangoldt_nonneg ArithmeticFunction.vonMangoldt_nonneg
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt_apply_pow /-
-theorem vonMangoldt_apply_pow {n k : ℕ} (hk : k ≠ 0) : Λ (n ^ k) = Λ n := by
+#print ArithmeticFunction.vonMangoldt_apply_pow /-
+theorem ArithmeticFunction.vonMangoldt_apply_pow {n k : ℕ} (hk : k ≠ 0) : Λ (n ^ k) = Λ n := by
   simp only [von_mangoldt_apply, isPrimePow_pow_iff hk, pow_min_fac hk]
-#align nat.arithmetic_function.von_mangoldt_apply_pow Nat.ArithmeticFunction.vonMangoldt_apply_pow
+#align nat.arithmetic_function.von_mangoldt_apply_pow ArithmeticFunction.vonMangoldt_apply_pow
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt_apply_prime /-
-theorem vonMangoldt_apply_prime {p : ℕ} (hp : p.Prime) : Λ p = Real.log p := by
+#print ArithmeticFunction.vonMangoldt_apply_prime /-
+theorem ArithmeticFunction.vonMangoldt_apply_prime {p : ℕ} (hp : p.Prime) : Λ p = Real.log p := by
   rw [von_mangoldt_apply, prime.min_fac_eq hp, if_pos hp.prime.is_prime_pow]
-#align nat.arithmetic_function.von_mangoldt_apply_prime Nat.ArithmeticFunction.vonMangoldt_apply_prime
+#align nat.arithmetic_function.von_mangoldt_apply_prime ArithmeticFunction.vonMangoldt_apply_prime
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt_ne_zero_iff /-
-theorem vonMangoldt_ne_zero_iff {n : ℕ} : Λ n ≠ 0 ↔ IsPrimePow n :=
+#print ArithmeticFunction.vonMangoldt_ne_zero_iff /-
+theorem ArithmeticFunction.vonMangoldt_ne_zero_iff {n : ℕ} : Λ n ≠ 0 ↔ IsPrimePow n :=
   by
   rcases eq_or_ne n 1 with (rfl | hn); · simp [not_isPrimePow_one]
   exact (Real.log_pos (one_lt_cast.2 (min_fac_prime hn).one_lt)).ne'.ite_ne_right_iff
-#align nat.arithmetic_function.von_mangoldt_ne_zero_iff Nat.ArithmeticFunction.vonMangoldt_ne_zero_iff
+#align nat.arithmetic_function.von_mangoldt_ne_zero_iff ArithmeticFunction.vonMangoldt_ne_zero_iff
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt_pos_iff /-
-theorem vonMangoldt_pos_iff {n : ℕ} : 0 < Λ n ↔ IsPrimePow n :=
-  vonMangoldt_nonneg.lt_iff_ne.trans (ne_comm.trans vonMangoldt_ne_zero_iff)
-#align nat.arithmetic_function.von_mangoldt_pos_iff Nat.ArithmeticFunction.vonMangoldt_pos_iff
+#print ArithmeticFunction.vonMangoldt_pos_iff /-
+theorem ArithmeticFunction.vonMangoldt_pos_iff {n : ℕ} : 0 < Λ n ↔ IsPrimePow n :=
+  ArithmeticFunction.vonMangoldt_nonneg.lt_iff_ne.trans
+    (ne_comm.trans ArithmeticFunction.vonMangoldt_ne_zero_iff)
+#align nat.arithmetic_function.von_mangoldt_pos_iff ArithmeticFunction.vonMangoldt_pos_iff
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt_eq_zero_iff /-
-theorem vonMangoldt_eq_zero_iff {n : ℕ} : Λ n = 0 ↔ ¬IsPrimePow n :=
-  vonMangoldt_ne_zero_iff.not_right
-#align nat.arithmetic_function.von_mangoldt_eq_zero_iff Nat.ArithmeticFunction.vonMangoldt_eq_zero_iff
+#print ArithmeticFunction.vonMangoldt_eq_zero_iff /-
+theorem ArithmeticFunction.vonMangoldt_eq_zero_iff {n : ℕ} : Λ n = 0 ↔ ¬IsPrimePow n :=
+  ArithmeticFunction.vonMangoldt_ne_zero_iff.not_right
+#align nat.arithmetic_function.von_mangoldt_eq_zero_iff ArithmeticFunction.vonMangoldt_eq_zero_iff
 -/
 
 open scoped BigOperators
 
-#print Nat.ArithmeticFunction.vonMangoldt_sum /-
-theorem vonMangoldt_sum {n : ℕ} : ∑ i in n.divisors, Λ i = Real.log n :=
+#print ArithmeticFunction.vonMangoldt_sum /-
+theorem ArithmeticFunction.vonMangoldt_sum {n : ℕ} : ∑ i in n.divisors, Λ i = Real.log n :=
   by
   refine' rec_on_prime_coprime _ _ _ n
   · simp
@@ -147,38 +149,40 @@ theorem vonMangoldt_sum {n : ℕ} : ∑ i in n.divisors, Λ i = Real.log n :=
   rw [mul_divisors_filter_prime_pow hab, filter_union,
     sum_union (disjoint_divisors_filter_prime_pow hab), ha, hb, Nat.cast_mul,
     Real.log_mul (cast_ne_zero.2 (pos_of_gt ha').ne') (cast_ne_zero.2 (pos_of_gt hb').ne')]
-#align nat.arithmetic_function.von_mangoldt_sum Nat.ArithmeticFunction.vonMangoldt_sum
+#align nat.arithmetic_function.von_mangoldt_sum ArithmeticFunction.vonMangoldt_sum
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt_mul_zeta /-
+#print ArithmeticFunction.vonMangoldt_mul_zeta /-
 @[simp]
-theorem vonMangoldt_mul_zeta : Λ * ζ = log := by ext n; rw [coe_mul_zeta_apply, von_mangoldt_sum];
-  rfl
-#align nat.arithmetic_function.von_mangoldt_mul_zeta Nat.ArithmeticFunction.vonMangoldt_mul_zeta
+theorem ArithmeticFunction.vonMangoldt_mul_zeta : Λ * ζ = ArithmeticFunction.log := by ext n;
+  rw [coe_mul_zeta_apply, von_mangoldt_sum]; rfl
+#align nat.arithmetic_function.von_mangoldt_mul_zeta ArithmeticFunction.vonMangoldt_mul_zeta
 -/
 
-#print Nat.ArithmeticFunction.zeta_mul_vonMangoldt /-
+#print ArithmeticFunction.zeta_mul_vonMangoldt /-
 @[simp]
-theorem zeta_mul_vonMangoldt : (ζ : ArithmeticFunction ℝ) * Λ = log := by rw [mul_comm]; simp
-#align nat.arithmetic_function.zeta_mul_von_mangoldt Nat.ArithmeticFunction.zeta_mul_vonMangoldt
+theorem ArithmeticFunction.zeta_mul_vonMangoldt :
+    (ζ : ArithmeticFunction ℝ) * Λ = ArithmeticFunction.log := by rw [mul_comm]; simp
+#align nat.arithmetic_function.zeta_mul_von_mangoldt ArithmeticFunction.zeta_mul_vonMangoldt
 -/
 
-#print Nat.ArithmeticFunction.log_mul_moebius_eq_vonMangoldt /-
+#print ArithmeticFunction.log_mul_moebius_eq_vonMangoldt /-
 @[simp]
-theorem log_mul_moebius_eq_vonMangoldt : log * μ = Λ := by
+theorem ArithmeticFunction.log_mul_moebius_eq_vonMangoldt : ArithmeticFunction.log * μ = Λ := by
   rw [← von_mangoldt_mul_zeta, mul_assoc, coe_zeta_mul_coe_moebius, mul_one]
-#align nat.arithmetic_function.log_mul_moebius_eq_von_mangoldt Nat.ArithmeticFunction.log_mul_moebius_eq_vonMangoldt
+#align nat.arithmetic_function.log_mul_moebius_eq_von_mangoldt ArithmeticFunction.log_mul_moebius_eq_vonMangoldt
 -/
 
-#print Nat.ArithmeticFunction.moebius_mul_log_eq_vonMangoldt /-
+#print ArithmeticFunction.moebius_mul_log_eq_vonMangoldt /-
 @[simp]
-theorem moebius_mul_log_eq_vonMangoldt : (μ : ArithmeticFunction ℝ) * log = Λ := by rw [mul_comm];
-  simp
-#align nat.arithmetic_function.moebius_mul_log_eq_von_mangoldt Nat.ArithmeticFunction.moebius_mul_log_eq_vonMangoldt
+theorem ArithmeticFunction.moebius_mul_log_eq_vonMangoldt :
+    (μ : ArithmeticFunction ℝ) * ArithmeticFunction.log = Λ := by rw [mul_comm]; simp
+#align nat.arithmetic_function.moebius_mul_log_eq_von_mangoldt ArithmeticFunction.moebius_mul_log_eq_vonMangoldt
 -/
 
-#print Nat.ArithmeticFunction.sum_moebius_mul_log_eq /-
-theorem sum_moebius_mul_log_eq {n : ℕ} : ∑ d in n.divisors, (μ d : ℝ) * log d = -Λ n :=
+#print ArithmeticFunction.sum_moebius_mul_log_eq /-
+theorem ArithmeticFunction.sum_moebius_mul_log_eq {n : ℕ} :
+    ∑ d in n.divisors, (μ d : ℝ) * ArithmeticFunction.log d = -Λ n :=
   by
   simp only [← log_mul_moebius_eq_von_mangoldt, mul_comm log, mul_apply, log_apply, int_coe_apply, ←
     Finset.sum_neg_distrib, neg_mul_eq_mul_neg]
@@ -198,16 +202,16 @@ theorem sum_moebius_mul_log_eq {n : ℕ} : ∑ d in n.divisors, (μ d : ℝ) * l
   rw [this, sum_sub_distrib, ← sum_mul, ← Int.cast_sum, ← coe_mul_zeta_apply, eq_comm, sub_eq_self,
     moebius_mul_coe_zeta, mul_eq_zero, Int.cast_eq_zero]
   rcases eq_or_ne n 1 with (hn | hn) <;> simp [hn]
-#align nat.arithmetic_function.sum_moebius_mul_log_eq Nat.ArithmeticFunction.sum_moebius_mul_log_eq
+#align nat.arithmetic_function.sum_moebius_mul_log_eq ArithmeticFunction.sum_moebius_mul_log_eq
 -/
 
-#print Nat.ArithmeticFunction.vonMangoldt_le_log /-
-theorem vonMangoldt_le_log : ∀ {n : ℕ}, Λ n ≤ Real.log (n : ℝ)
+#print ArithmeticFunction.vonMangoldt_le_log /-
+theorem ArithmeticFunction.vonMangoldt_le_log : ∀ {n : ℕ}, Λ n ≤ Real.log (n : ℝ)
   | 0 => by simp
   | n + 1 => by
     rw [← von_mangoldt_sum]
     exact single_le_sum (fun _ _ => von_mangoldt_nonneg) (mem_divisors_self _ n.succ_ne_zero)
-#align nat.arithmetic_function.von_mangoldt_le_log Nat.ArithmeticFunction.vonMangoldt_le_log
+#align nat.arithmetic_function.von_mangoldt_le_log ArithmeticFunction.vonMangoldt_le_log
 -/
 
 end ArithmeticFunction

61b5e275

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
-import Mathbin.Algebra.IsPrimePow
-import Mathbin.NumberTheory.ArithmeticFunction
-import Mathbin.Analysis.SpecialFunctions.Log.Basic
+import Algebra.IsPrimePow
+import NumberTheory.ArithmeticFunction
+import Analysis.SpecialFunctions.Log.Basic
 
 #align_import number_theory.von_mangoldt from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"

61b5e275

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module number_theory.von_mangoldt
-! leanprover-community/mathlib commit 61b5e2755ccb464b68d05a9acf891ae04992d09d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.IsPrimePow
 import Mathbin.NumberTheory.ArithmeticFunction
 import Mathbin.Analysis.SpecialFunctions.Log.Basic
 
+#align_import number_theory.von_mangoldt from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"
+
 /-!
 # The von Mangoldt Function

61b5e275

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -47,18 +47,23 @@ open Finset
 
 open scoped ArithmeticFunction
 
+#print Nat.ArithmeticFunction.log /-
 /-- `log` as an arithmetic function `ℕ → ℝ`. Note this is in the `nat.arithmetic_function`
 namespace to indicate that it is bundled as an `arithmetic_function` rather than being the usual
 real logarithm. -/
 noncomputable def log : ArithmeticFunction ℝ :=
   ⟨fun n => Real.log n, by simp⟩
 #align nat.arithmetic_function.log Nat.ArithmeticFunction.log
+-/
 
+#print Nat.ArithmeticFunction.log_apply /-
 @[simp]
 theorem log_apply {n : ℕ} : log n = Real.log n :=
   rfl
 #align nat.arithmetic_function.log_apply Nat.ArithmeticFunction.log_apply
+-/
 
+#print Nat.ArithmeticFunction.vonMangoldt /-
 /--
 The `von_mangoldt` function is the function on natural numbers that returns `log p` if the input can
 be expressed as `p^k` for a prime `p`.
@@ -70,18 +75,23 @@ In the `arithmetic_function` locale, we have the notation `Λ` for this function
 noncomputable def vonMangoldt : ArithmeticFunction ℝ :=
   ⟨fun n => if IsPrimePow n then Real.log (minFac n) else 0, if_neg not_isPrimePow_zero⟩
 #align nat.arithmetic_function.von_mangoldt Nat.ArithmeticFunction.vonMangoldt
+-/
 
--- mathport name: von_mangoldt
 scoped[ArithmeticFunction] notation "Λ" => Nat.ArithmeticFunction.vonMangoldt
 
+#print Nat.ArithmeticFunction.vonMangoldt_apply /-
 theorem vonMangoldt_apply {n : ℕ} : Λ n = if IsPrimePow n then Real.log (minFac n) else 0 :=
   rfl
 #align nat.arithmetic_function.von_mangoldt_apply Nat.ArithmeticFunction.vonMangoldt_apply
+-/
 
+#print Nat.ArithmeticFunction.vonMangoldt_apply_one /-
 @[simp]
 theorem vonMangoldt_apply_one : Λ 1 = 0 := by simp [von_mangoldt_apply]
 #align nat.arithmetic_function.von_mangoldt_apply_one Nat.ArithmeticFunction.vonMangoldt_apply_one
+-/
 
+#print Nat.ArithmeticFunction.vonMangoldt_nonneg /-
 @[simp]
 theorem vonMangoldt_nonneg {n : ℕ} : 0 ≤ Λ n :=
   by
@@ -90,6 +100,7 @@ theorem vonMangoldt_nonneg {n : ℕ} : 0 ≤ Λ n :=
   · exact Real.log_nonneg (one_le_cast.2 (Nat.minFac_pos n))
   rfl
 #align nat.arithmetic_function.von_mangoldt_nonneg Nat.ArithmeticFunction.vonMangoldt_nonneg
+-/
 
 #print Nat.ArithmeticFunction.vonMangoldt_apply_pow /-
 theorem vonMangoldt_apply_pow {n k : ℕ} (hk : k ≠ 0) : Λ (n ^ k) = Λ n := by
@@ -97,26 +108,35 @@ theorem vonMangoldt_apply_pow {n k : ℕ} (hk : k ≠ 0) : Λ (n ^ k) = Λ n :=
 #align nat.arithmetic_function.von_mangoldt_apply_pow Nat.ArithmeticFunction.vonMangoldt_apply_pow
 -/
 
+#print Nat.ArithmeticFunction.vonMangoldt_apply_prime /-
 theorem vonMangoldt_apply_prime {p : ℕ} (hp : p.Prime) : Λ p = Real.log p := by
   rw [von_mangoldt_apply, prime.min_fac_eq hp, if_pos hp.prime.is_prime_pow]
 #align nat.arithmetic_function.von_mangoldt_apply_prime Nat.ArithmeticFunction.vonMangoldt_apply_prime
+-/
 
+#print Nat.ArithmeticFunction.vonMangoldt_ne_zero_iff /-
 theorem vonMangoldt_ne_zero_iff {n : ℕ} : Λ n ≠ 0 ↔ IsPrimePow n :=
   by
   rcases eq_or_ne n 1 with (rfl | hn); · simp [not_isPrimePow_one]
   exact (Real.log_pos (one_lt_cast.2 (min_fac_prime hn).one_lt)).ne'.ite_ne_right_iff
 #align nat.arithmetic_function.von_mangoldt_ne_zero_iff Nat.ArithmeticFunction.vonMangoldt_ne_zero_iff
+-/
 
+#print Nat.ArithmeticFunction.vonMangoldt_pos_iff /-
 theorem vonMangoldt_pos_iff {n : ℕ} : 0 < Λ n ↔ IsPrimePow n :=
   vonMangoldt_nonneg.lt_iff_ne.trans (ne_comm.trans vonMangoldt_ne_zero_iff)
 #align nat.arithmetic_function.von_mangoldt_pos_iff Nat.ArithmeticFunction.vonMangoldt_pos_iff
+-/
 
+#print Nat.ArithmeticFunction.vonMangoldt_eq_zero_iff /-
 theorem vonMangoldt_eq_zero_iff {n : ℕ} : Λ n = 0 ↔ ¬IsPrimePow n :=
   vonMangoldt_ne_zero_iff.not_right
 #align nat.arithmetic_function.von_mangoldt_eq_zero_iff Nat.ArithmeticFunction.vonMangoldt_eq_zero_iff
+-/
 
 open scoped BigOperators
 
+#print Nat.ArithmeticFunction.vonMangoldt_sum /-
 theorem vonMangoldt_sum {n : ℕ} : ∑ i in n.divisors, Λ i = Real.log n :=
   by
   refine' rec_on_prime_coprime _ _ _ n
@@ -131,26 +151,36 @@ theorem vonMangoldt_sum {n : ℕ} : ∑ i in n.divisors, Λ i = Real.log n :=
     sum_union (disjoint_divisors_filter_prime_pow hab), ha, hb, Nat.cast_mul,
     Real.log_mul (cast_ne_zero.2 (pos_of_gt ha').ne') (cast_ne_zero.2 (pos_of_gt hb').ne')]
 #align nat.arithmetic_function.von_mangoldt_sum Nat.ArithmeticFunction.vonMangoldt_sum
+-/
 
+#print Nat.ArithmeticFunction.vonMangoldt_mul_zeta /-
 @[simp]
 theorem vonMangoldt_mul_zeta : Λ * ζ = log := by ext n; rw [coe_mul_zeta_apply, von_mangoldt_sum];
   rfl
 #align nat.arithmetic_function.von_mangoldt_mul_zeta Nat.ArithmeticFunction.vonMangoldt_mul_zeta
+-/
 
+#print Nat.ArithmeticFunction.zeta_mul_vonMangoldt /-
 @[simp]
 theorem zeta_mul_vonMangoldt : (ζ : ArithmeticFunction ℝ) * Λ = log := by rw [mul_comm]; simp
 #align nat.arithmetic_function.zeta_mul_von_mangoldt Nat.ArithmeticFunction.zeta_mul_vonMangoldt
+-/
 
+#print Nat.ArithmeticFunction.log_mul_moebius_eq_vonMangoldt /-
 @[simp]
 theorem log_mul_moebius_eq_vonMangoldt : log * μ = Λ := by
   rw [← von_mangoldt_mul_zeta, mul_assoc, coe_zeta_mul_coe_moebius, mul_one]
 #align nat.arithmetic_function.log_mul_moebius_eq_von_mangoldt Nat.ArithmeticFunction.log_mul_moebius_eq_vonMangoldt
+-/
 
+#print Nat.ArithmeticFunction.moebius_mul_log_eq_vonMangoldt /-
 @[simp]
 theorem moebius_mul_log_eq_vonMangoldt : (μ : ArithmeticFunction ℝ) * log = Λ := by rw [mul_comm];
   simp
 #align nat.arithmetic_function.moebius_mul_log_eq_von_mangoldt Nat.ArithmeticFunction.moebius_mul_log_eq_vonMangoldt
+-/
 
+#print Nat.ArithmeticFunction.sum_moebius_mul_log_eq /-
 theorem sum_moebius_mul_log_eq {n : ℕ} : ∑ d in n.divisors, (μ d : ℝ) * log d = -Λ n :=
   by
   simp only [← log_mul_moebius_eq_von_mangoldt, mul_comm log, mul_apply, log_apply, int_coe_apply, ←
@@ -172,13 +202,16 @@ theorem sum_moebius_mul_log_eq {n : ℕ} : ∑ d in n.divisors, (μ d : ℝ) * l
     moebius_mul_coe_zeta, mul_eq_zero, Int.cast_eq_zero]
   rcases eq_or_ne n 1 with (hn | hn) <;> simp [hn]
 #align nat.arithmetic_function.sum_moebius_mul_log_eq Nat.ArithmeticFunction.sum_moebius_mul_log_eq
+-/
 
+#print Nat.ArithmeticFunction.vonMangoldt_le_log /-
 theorem vonMangoldt_le_log : ∀ {n : ℕ}, Λ n ≤ Real.log (n : ℝ)
   | 0 => by simp
   | n + 1 => by
     rw [← von_mangoldt_sum]
     exact single_le_sum (fun _ _ => von_mangoldt_nonneg) (mem_divisors_self _ n.succ_ne_zero)
 #align nat.arithmetic_function.von_mangoldt_le_log Nat.ArithmeticFunction.vonMangoldt_le_log
+-/
 
 end ArithmeticFunction

61b5e275

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -117,7 +117,7 @@ theorem vonMangoldt_eq_zero_iff {n : ℕ} : Λ n = 0 ↔ ¬IsPrimePow n :=
 
 open scoped BigOperators
 
-theorem vonMangoldt_sum {n : ℕ} : (∑ i in n.divisors, Λ i) = Real.log n :=
+theorem vonMangoldt_sum {n : ℕ} : ∑ i in n.divisors, Λ i = Real.log n :=
   by
   refine' rec_on_prime_coprime _ _ _ n
   · simp
@@ -151,14 +151,14 @@ theorem moebius_mul_log_eq_vonMangoldt : (μ : ArithmeticFunction ℝ) * log = 
   simp
 #align nat.arithmetic_function.moebius_mul_log_eq_von_mangoldt Nat.ArithmeticFunction.moebius_mul_log_eq_vonMangoldt
 
-theorem sum_moebius_mul_log_eq {n : ℕ} : (∑ d in n.divisors, (μ d : ℝ) * log d) = -Λ n :=
+theorem sum_moebius_mul_log_eq {n : ℕ} : ∑ d in n.divisors, (μ d : ℝ) * log d = -Λ n :=
   by
   simp only [← log_mul_moebius_eq_von_mangoldt, mul_comm log, mul_apply, log_apply, int_coe_apply, ←
     Finset.sum_neg_distrib, neg_mul_eq_mul_neg]
   rw [sum_divisors_antidiagonal fun i j => (μ i : ℝ) * -Real.log j]
   have :
-    (∑ i : ℕ in n.divisors, (μ i : ℝ) * -Real.log (n / i : ℕ)) =
-      ∑ i : ℕ in n.divisors, (μ i : ℝ) * Real.log i - μ i * Real.log n :=
+    ∑ i : ℕ in n.divisors, (μ i : ℝ) * -Real.log (n / i : ℕ) =
+      ∑ i : ℕ in n.divisors, ((μ i : ℝ) * Real.log i - μ i * Real.log n) :=
     by
     apply sum_congr rfl
     simp only [and_imp, Int.cast_eq_zero, mul_eq_mul_left_iff, Ne.def, neg_inj, mem_divisors]

61b5e275

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -126,7 +126,7 @@ theorem vonMangoldt_sum {n : ℕ} : (∑ i in n.divisors, Λ i) = Real.log n :=
       von_mangoldt_apply_one]
     simp [von_mangoldt_apply_pow (Nat.succ_ne_zero _), von_mangoldt_apply_prime hp]
   intro a b ha' hb' hab ha hb
-  simp only [von_mangoldt_apply, ← sum_filter] at ha hb⊢
+  simp only [von_mangoldt_apply, ← sum_filter] at ha hb ⊢
   rw [mul_divisors_filter_prime_pow hab, filter_union,
     sum_union (disjoint_divisors_filter_prime_pow hab), ha, hb, Nat.cast_mul,
     Real.log_mul (cast_ne_zero.2 (pos_of_gt ha').ne') (cast_ne_zero.2 (pos_of_gt hb').ne')]

61b5e275

bump to nightly-2023-06-01-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

4d9eaa85

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 
 ! This file was ported from Lean 3 source module number_theory.von_mangoldt
-! leanprover-community/mathlib commit c946d6097a6925ad16d7ec55677bbc977f9846de
+! leanprover-community/mathlib commit 61b5e2755ccb464b68d05a9acf891ae04992d09d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.SpecialFunctions.Log.Basic
 /-!
 # The von Mangoldt Function
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define the von Mangoldt function: the function on natural numbers that returns
 `log p` if the input can be expressed as `p^k` for a prime `p`.
 
@@ -88,9 +91,11 @@ theorem vonMangoldt_nonneg {n : ℕ} : 0 ≤ Λ n :=
   rfl
 #align nat.arithmetic_function.von_mangoldt_nonneg Nat.ArithmeticFunction.vonMangoldt_nonneg
 
+#print Nat.ArithmeticFunction.vonMangoldt_apply_pow /-
 theorem vonMangoldt_apply_pow {n k : ℕ} (hk : k ≠ 0) : Λ (n ^ k) = Λ n := by
   simp only [von_mangoldt_apply, isPrimePow_pow_iff hk, pow_min_fac hk]
 #align nat.arithmetic_function.von_mangoldt_apply_pow Nat.ArithmeticFunction.vonMangoldt_apply_pow
+-/
 
 theorem vonMangoldt_apply_prime {p : ℕ} (hp : p.Prime) : Λ p = Real.log p := by
   rw [von_mangoldt_apply, prime.min_fac_eq hp, if_pos hp.prime.is_prime_pow]

c946d609

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -42,7 +42,7 @@ namespace ArithmeticFunction
 
 open Finset
 
-open ArithmeticFunction
+open scoped ArithmeticFunction
 
 /-- `log` as an arithmetic function `ℕ → ℝ`. Note this is in the `nat.arithmetic_function`
 namespace to indicate that it is bundled as an `arithmetic_function` rather than being the usual
@@ -110,7 +110,7 @@ theorem vonMangoldt_eq_zero_iff {n : ℕ} : Λ n = 0 ↔ ¬IsPrimePow n :=
   vonMangoldt_ne_zero_iff.not_right
 #align nat.arithmetic_function.von_mangoldt_eq_zero_iff Nat.ArithmeticFunction.vonMangoldt_eq_zero_iff
 
-open BigOperators
+open scoped BigOperators
 
 theorem vonMangoldt_sum {n : ℕ} : (∑ i in n.divisors, Λ i) = Real.log n :=
   by

c946d609

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -128,17 +128,12 @@ theorem vonMangoldt_sum {n : ℕ} : (∑ i in n.divisors, Λ i) = Real.log n :=
 #align nat.arithmetic_function.von_mangoldt_sum Nat.ArithmeticFunction.vonMangoldt_sum
 
 @[simp]
-theorem vonMangoldt_mul_zeta : Λ * ζ = log := by
-  ext n
-  rw [coe_mul_zeta_apply, von_mangoldt_sum]
+theorem vonMangoldt_mul_zeta : Λ * ζ = log := by ext n; rw [coe_mul_zeta_apply, von_mangoldt_sum];
   rfl
 #align nat.arithmetic_function.von_mangoldt_mul_zeta Nat.ArithmeticFunction.vonMangoldt_mul_zeta
 
 @[simp]
-theorem zeta_mul_vonMangoldt : (ζ : ArithmeticFunction ℝ) * Λ = log :=
-  by
-  rw [mul_comm]
-  simp
+theorem zeta_mul_vonMangoldt : (ζ : ArithmeticFunction ℝ) * Λ = log := by rw [mul_comm]; simp
 #align nat.arithmetic_function.zeta_mul_von_mangoldt Nat.ArithmeticFunction.zeta_mul_vonMangoldt
 
 @[simp]
@@ -147,9 +142,7 @@ theorem log_mul_moebius_eq_vonMangoldt : log * μ = Λ := by
 #align nat.arithmetic_function.log_mul_moebius_eq_von_mangoldt Nat.ArithmeticFunction.log_mul_moebius_eq_vonMangoldt
 
 @[simp]
-theorem moebius_mul_log_eq_vonMangoldt : (μ : ArithmeticFunction ℝ) * log = Λ :=
-  by
-  rw [mul_comm]
+theorem moebius_mul_log_eq_vonMangoldt : (μ : ArithmeticFunction ℝ) * log = Λ := by rw [mul_comm];
   simp
 #align nat.arithmetic_function.moebius_mul_log_eq_von_mangoldt Nat.ArithmeticFunction.moebius_mul_log_eq_vonMangoldt

c946d609

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

c946d609

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11813)

08686b25

Diff

@@ -150,7 +150,7 @@ theorem sum_moebius_mul_log_eq {n : ℕ} : (∑ d in n.divisors, (μ d : ℝ) *
   have : (∑ i : ℕ in n.divisors, (μ i : ℝ) * -Real.log (n / i : ℕ)) =
       ∑ i : ℕ in n.divisors, ((μ i : ℝ) * Real.log i - μ i * Real.log n) := by
     apply sum_congr rfl
-    simp only [and_imp, Int.cast_eq_zero, mul_eq_mul_left_iff, Ne.def, neg_inj, mem_divisors]
+    simp only [and_imp, Int.cast_eq_zero, mul_eq_mul_left_iff, Ne, neg_inj, mem_divisors]
     intro m mn hn
     have : (m : ℝ) ≠ 0 := by
       rw [cast_ne_zero]

c946d609

feat(NumberTheory/ArithmeticFunction): add separate scopes for notations (and a lemma) (#10403)

This adds individual scopes ArithmeticFunction.zeta, ..., ArithmeticFunction.Omega, ArithmeticFunction.Moebius, ArithmeticFunction.vonMangoldt for the notations ζ, σ, ω, Ω and μ, Λ. This makes it possible to access a selected subset of these instead of either none or all of them.

We also add the lemma ArithmeticFunction.pmul_assoc.

See here and here on Zulip.

f9d86759

Diff

@@ -29,6 +29,8 @@ to deduce alternative expressions for the von Mangoldt function via Möbius inve
 ## Notation
 
 We use the standard notation `Λ` to represent the von Mangoldt function.
+It is accessible in the locales `ArithmeticFunction` (like the notations for other arithmetic
+functions) and also in the locale `ArithmeticFunction.vonMangoldt`.
 
 -/
 
@@ -57,6 +59,8 @@ In the case when `n` is a prime power, `min_fac` will give the appropriate prime
 smallest prime factor.
 
 In the `ArithmeticFunction` locale, we have the notation `Λ` for this function.
+This is also available in the `ArithmeticFunction.vonMangoldt` locale, allowing for selective
+access to the notation.
 -/
 noncomputable def vonMangoldt : ArithmeticFunction ℝ :=
   ⟨fun n => if IsPrimePow n then Real.log (minFac n) else 0, if_neg not_isPrimePow_zero⟩
@@ -64,6 +68,9 @@ noncomputable def vonMangoldt : ArithmeticFunction ℝ :=
 
 @[inherit_doc] scoped[ArithmeticFunction] notation "Λ" => ArithmeticFunction.vonMangoldt
 
+@[inherit_doc] scoped[ArithmeticFunction.vonMangoldt] notation "Λ" =>
+  ArithmeticFunction.vonMangoldt
+
 theorem vonMangoldt_apply {n : ℕ} : Λ n = if IsPrimePow n then Real.log (minFac n) else 0 :=
   rfl
 #align nat.arithmetic_function.von_mangoldt_apply ArithmeticFunction.vonMangoldt_apply

c946d609

chore(NumberTheory/ArithmeticFunction): remove Nat. part from ArithmeticFunction namespace (#10399)

This changes Nat.ArithmeticFunction to ArithmeticFunction since the Nat part seems redundant.

See here on Zulip.

a6a17daf

Diff

@@ -19,12 +19,12 @@ In this file we define the von Mangoldt function: the function on natural number
 
 The main definition for this file is
 
-- `Nat.ArithmeticFunction.vonMangoldt`: The von Mangoldt function `Λ`.
+- `ArithmeticFunction.vonMangoldt`: The von Mangoldt function `Λ`.
 
 We then prove the classical summation property of the von Mangoldt function in
-`Nat.ArithmeticFunction.vonMangoldt_sum`, that `∑ i in n.divisors, Λ i = Real.log n`, and use this
+`ArithmeticFunction.vonMangoldt_sum`, that `∑ i in n.divisors, Λ i = Real.log n`, and use this
 to deduce alternative expressions for the von Mangoldt function via Möbius inversion, see
-`Nat.ArithmeticFunction.sum_moebius_mul_log_eq`.
+`ArithmeticFunction.sum_moebius_mul_log_eq`.
 
 ## Notation
 
@@ -32,26 +32,23 @@ We use the standard notation `Λ` to represent the von Mangoldt function.
 
 -/
 
-
-namespace Nat
-
 namespace ArithmeticFunction
 
-open Finset
+open Finset Nat
 
 open scoped ArithmeticFunction
 
-/-- `log` as an arithmetic function `ℕ → ℝ`. Note this is in the `Nat.ArithmeticFunction`
+/-- `log` as an arithmetic function `ℕ → ℝ`. Note this is in the `ArithmeticFunction`
 namespace to indicate that it is bundled as an `ArithmeticFunction` rather than being the usual
 real logarithm. -/
 noncomputable def log : ArithmeticFunction ℝ :=
   ⟨fun n => Real.log n, by simp⟩
-#align nat.arithmetic_function.log Nat.ArithmeticFunction.log
+#align nat.arithmetic_function.log ArithmeticFunction.log
 
 @[simp]
 theorem log_apply {n : ℕ} : log n = Real.log n :=
   rfl
-#align nat.arithmetic_function.log_apply Nat.ArithmeticFunction.log_apply
+#align nat.arithmetic_function.log_apply ArithmeticFunction.log_apply
 
 /--
 The `vonMangoldt` function is the function on natural numbers that returns `log p` if the input can
@@ -63,17 +60,17 @@ In the `ArithmeticFunction` locale, we have the notation `Λ` for this function.
 -/
 noncomputable def vonMangoldt : ArithmeticFunction ℝ :=
   ⟨fun n => if IsPrimePow n then Real.log (minFac n) else 0, if_neg not_isPrimePow_zero⟩
-#align nat.arithmetic_function.von_mangoldt Nat.ArithmeticFunction.vonMangoldt
+#align nat.arithmetic_function.von_mangoldt ArithmeticFunction.vonMangoldt
 
-@[inherit_doc] scoped[Nat.ArithmeticFunction] notation "Λ" => Nat.ArithmeticFunction.vonMangoldt
+@[inherit_doc] scoped[ArithmeticFunction] notation "Λ" => ArithmeticFunction.vonMangoldt
 
 theorem vonMangoldt_apply {n : ℕ} : Λ n = if IsPrimePow n then Real.log (minFac n) else 0 :=
   rfl
-#align nat.arithmetic_function.von_mangoldt_apply Nat.ArithmeticFunction.vonMangoldt_apply
+#align nat.arithmetic_function.von_mangoldt_apply ArithmeticFunction.vonMangoldt_apply
 
 @[simp]
 theorem vonMangoldt_apply_one : Λ 1 = 0 := by simp [vonMangoldt_apply]
-#align nat.arithmetic_function.von_mangoldt_apply_one Nat.ArithmeticFunction.vonMangoldt_apply_one
+#align nat.arithmetic_function.von_mangoldt_apply_one ArithmeticFunction.vonMangoldt_apply_one
 
 @[simp]
 theorem vonMangoldt_nonneg {n : ℕ} : 0 ≤ Λ n := by
@@ -81,28 +78,28 @@ theorem vonMangoldt_nonneg {n : ℕ} : 0 ≤ Λ n := by
   split_ifs
   · exact Real.log_nonneg (one_le_cast.2 (Nat.minFac_pos n))
   rfl
-#align nat.arithmetic_function.von_mangoldt_nonneg Nat.ArithmeticFunction.vonMangoldt_nonneg
+#align nat.arithmetic_function.von_mangoldt_nonneg ArithmeticFunction.vonMangoldt_nonneg
 
 theorem vonMangoldt_apply_pow {n k : ℕ} (hk : k ≠ 0) : Λ (n ^ k) = Λ n := by
   simp only [vonMangoldt_apply, isPrimePow_pow_iff hk, pow_minFac hk]
-#align nat.arithmetic_function.von_mangoldt_apply_pow Nat.ArithmeticFunction.vonMangoldt_apply_pow
+#align nat.arithmetic_function.von_mangoldt_apply_pow ArithmeticFunction.vonMangoldt_apply_pow
 
 theorem vonMangoldt_apply_prime {p : ℕ} (hp : p.Prime) : Λ p = Real.log p := by
   rw [vonMangoldt_apply, Prime.minFac_eq hp, if_pos hp.prime.isPrimePow]
-#align nat.arithmetic_function.von_mangoldt_apply_prime Nat.ArithmeticFunction.vonMangoldt_apply_prime
+#align nat.arithmetic_function.von_mangoldt_apply_prime ArithmeticFunction.vonMangoldt_apply_prime
 
 theorem vonMangoldt_ne_zero_iff {n : ℕ} : Λ n ≠ 0 ↔ IsPrimePow n := by
   rcases eq_or_ne n 1 with (rfl | hn); · simp [not_isPrimePow_one]
   exact (Real.log_pos (one_lt_cast.2 (minFac_prime hn).one_lt)).ne'.ite_ne_right_iff
-#align nat.arithmetic_function.von_mangoldt_ne_zero_iff Nat.ArithmeticFunction.vonMangoldt_ne_zero_iff
+#align nat.arithmetic_function.von_mangoldt_ne_zero_iff ArithmeticFunction.vonMangoldt_ne_zero_iff
 
 theorem vonMangoldt_pos_iff {n : ℕ} : 0 < Λ n ↔ IsPrimePow n :=
   vonMangoldt_nonneg.lt_iff_ne.trans (ne_comm.trans vonMangoldt_ne_zero_iff)
-#align nat.arithmetic_function.von_mangoldt_pos_iff Nat.ArithmeticFunction.vonMangoldt_pos_iff
+#align nat.arithmetic_function.von_mangoldt_pos_iff ArithmeticFunction.vonMangoldt_pos_iff
 
 theorem vonMangoldt_eq_zero_iff {n : ℕ} : Λ n = 0 ↔ ¬IsPrimePow n :=
   vonMangoldt_ne_zero_iff.not_right
-#align nat.arithmetic_function.von_mangoldt_eq_zero_iff Nat.ArithmeticFunction.vonMangoldt_eq_zero_iff
+#align nat.arithmetic_function.von_mangoldt_eq_zero_iff ArithmeticFunction.vonMangoldt_eq_zero_iff
 
 open scoped BigOperators
 
@@ -110,7 +107,7 @@ theorem vonMangoldt_sum {n : ℕ} : ∑ i in n.divisors, Λ i = Real.log n := by
   refine' recOnPrimeCoprime _ _ _ n
   · simp
   · intro p k hp
-    rw [sum_divisors_prime_pow hp, cast_pow, Real.log_pow, Finset.sum_range_succ', pow_zero,
+    rw [sum_divisors_prime_pow hp, cast_pow, Real.log_pow, Finset.sum_range_succ', Nat.pow_zero,
       vonMangoldt_apply_one]
     simp [vonMangoldt_apply_pow (Nat.succ_ne_zero _), vonMangoldt_apply_prime hp]
   intro a b ha' hb' hab ha hb
@@ -118,26 +115,26 @@ theorem vonMangoldt_sum {n : ℕ} : ∑ i in n.divisors, Λ i = Real.log n := by
   rw [mul_divisors_filter_prime_pow hab, filter_union,
     sum_union (disjoint_divisors_filter_isPrimePow hab), ha, hb, Nat.cast_mul,
     Real.log_mul (cast_ne_zero.2 (pos_of_gt ha').ne') (cast_ne_zero.2 (pos_of_gt hb').ne')]
-#align nat.arithmetic_function.von_mangoldt_sum Nat.ArithmeticFunction.vonMangoldt_sum
+#align nat.arithmetic_function.von_mangoldt_sum ArithmeticFunction.vonMangoldt_sum
 
 @[simp]
 theorem vonMangoldt_mul_zeta : Λ * ζ = log := by
   ext n; rw [coe_mul_zeta_apply, vonMangoldt_sum]; rfl
-#align nat.arithmetic_function.von_mangoldt_mul_zeta Nat.ArithmeticFunction.vonMangoldt_mul_zeta
+#align nat.arithmetic_function.von_mangoldt_mul_zeta ArithmeticFunction.vonMangoldt_mul_zeta
 
 @[simp]
 theorem zeta_mul_vonMangoldt : (ζ : ArithmeticFunction ℝ) * Λ = log := by rw [mul_comm]; simp
-#align nat.arithmetic_function.zeta_mul_von_mangoldt Nat.ArithmeticFunction.zeta_mul_vonMangoldt
+#align nat.arithmetic_function.zeta_mul_von_mangoldt ArithmeticFunction.zeta_mul_vonMangoldt
 
 @[simp]
 theorem log_mul_moebius_eq_vonMangoldt : log * μ = Λ := by
   rw [← vonMangoldt_mul_zeta, mul_assoc, coe_zeta_mul_coe_moebius, mul_one]
-#align nat.arithmetic_function.log_mul_moebius_eq_von_mangoldt Nat.ArithmeticFunction.log_mul_moebius_eq_vonMangoldt
+#align nat.arithmetic_function.log_mul_moebius_eq_von_mangoldt ArithmeticFunction.log_mul_moebius_eq_vonMangoldt
 
 @[simp]
 theorem moebius_mul_log_eq_vonMangoldt : (μ : ArithmeticFunction ℝ) * log = Λ := by
   rw [mul_comm]; simp
-#align nat.arithmetic_function.moebius_mul_log_eq_von_mangoldt Nat.ArithmeticFunction.moebius_mul_log_eq_vonMangoldt
+#align nat.arithmetic_function.moebius_mul_log_eq_von_mangoldt ArithmeticFunction.moebius_mul_log_eq_vonMangoldt
 
 theorem sum_moebius_mul_log_eq {n : ℕ} : (∑ d in n.divisors, (μ d : ℝ) * log d) = -Λ n := by
   simp only [← log_mul_moebius_eq_vonMangoldt, mul_comm log, mul_apply, log_apply, intCoe_apply, ←
@@ -156,7 +153,7 @@ theorem sum_moebius_mul_log_eq {n : ℕ} : (∑ d in n.divisors, (μ d : ℝ) *
   rw [this, sum_sub_distrib, ← sum_mul, ← Int.cast_sum, ← coe_mul_zeta_apply, eq_comm, sub_eq_self,
     moebius_mul_coe_zeta]
   rcases eq_or_ne n 1 with (hn | hn) <;> simp [hn]
-#align nat.arithmetic_function.sum_moebius_mul_log_eq Nat.ArithmeticFunction.sum_moebius_mul_log_eq
+#align nat.arithmetic_function.sum_moebius_mul_log_eq ArithmeticFunction.sum_moebius_mul_log_eq
 
 theorem vonMangoldt_le_log : ∀ {n : ℕ}, Λ n ≤ Real.log (n : ℝ)
   | 0 => by simp
@@ -164,8 +161,6 @@ theorem vonMangoldt_le_log : ∀ {n : ℕ}, Λ n ≤ Real.log (n : ℝ)
     rw [← vonMangoldt_sum]
     exact single_le_sum (by exact fun _ _ => vonMangoldt_nonneg)
       (mem_divisors_self _ n.succ_ne_zero)
-#align nat.arithmetic_function.von_mangoldt_le_log Nat.ArithmeticFunction.vonMangoldt_le_log
+#align nat.arithmetic_function.von_mangoldt_le_log ArithmeticFunction.vonMangoldt_le_log
 
 end ArithmeticFunction
-
-end Nat

c946d609

doc: @[inherit_doc] on notations (#9942)

Make all the notations that unambiguously should inherit the docstring of their definition actually inherit it.

Also write a few docstrings by hand. I only wrote the ones I was competent to write and which I was sure of. Some docstrings come from mathlib3 as they were lost during the early port.

This PR is only intended as a first pass There are many more docstrings to add.

08f7e99d

Diff

@@ -65,7 +65,7 @@ noncomputable def vonMangoldt : ArithmeticFunction ℝ :=
   ⟨fun n => if IsPrimePow n then Real.log (minFac n) else 0, if_neg not_isPrimePow_zero⟩
 #align nat.arithmetic_function.von_mangoldt Nat.ArithmeticFunction.vonMangoldt
 
-scoped[Nat.ArithmeticFunction] notation "Λ" => Nat.ArithmeticFunction.vonMangoldt
+@[inherit_doc] scoped[Nat.ArithmeticFunction] notation "Λ" => Nat.ArithmeticFunction.vonMangoldt
 
 theorem vonMangoldt_apply {n : ℕ} : Λ n = if IsPrimePow n then Real.log (minFac n) else 0 :=
   rfl

c946d609

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module number_theory.von_mangoldt
-! leanprover-community/mathlib commit c946d6097a6925ad16d7ec55677bbc977f9846de
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.IsPrimePow
 import Mathlib.NumberTheory.ArithmeticFunction
 import Mathlib.Analysis.SpecialFunctions.Log.Basic
 
+#align_import number_theory.von_mangoldt from "leanprover-community/mathlib"@"c946d6097a6925ad16d7ec55677bbc977f9846de"
+
 /-!
 # The von Mangoldt Function

c946d609

fix: ∑' precedence (#5615)

Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) $([∑∏][^()∑∏]*,[^()∑∏:]*)$ ([⊂⊆=<≤]) replaced by $1 $2 $3

03fc68aa

Diff

@@ -109,7 +109,7 @@ theorem vonMangoldt_eq_zero_iff {n : ℕ} : Λ n = 0 ↔ ¬IsPrimePow n :=
 
 open scoped BigOperators
 
-theorem vonMangoldt_sum {n : ℕ} : (∑ i in n.divisors, Λ i) = Real.log n := by
+theorem vonMangoldt_sum {n : ℕ} : ∑ i in n.divisors, Λ i = Real.log n := by
   refine' recOnPrimeCoprime _ _ _ n
   · simp
   · intro p k hp

c946d609

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -117,7 +117,7 @@ theorem vonMangoldt_sum {n : ℕ} : (∑ i in n.divisors, Λ i) = Real.log n :=
       vonMangoldt_apply_one]
     simp [vonMangoldt_apply_pow (Nat.succ_ne_zero _), vonMangoldt_apply_prime hp]
   intro a b ha' hb' hab ha hb
-  simp only [vonMangoldt_apply, ← sum_filter] at ha hb⊢
+  simp only [vonMangoldt_apply, ← sum_filter] at ha hb ⊢
   rw [mul_divisors_filter_prime_pow hab, filter_union,
     sum_union (disjoint_divisors_filter_isPrimePow hab), ha, hb, Nat.cast_mul,
     Real.log_mul (cast_ne_zero.2 (pos_of_gt ha').ne') (cast_ne_zero.2 (pos_of_gt hb').ne')]

c946d609

feat: port NumberTheory.VonMangoldt (#4494)

541bcf2b

`number_theory.von_mangoldt` ⟷ `Mathlib.NumberTheory.VonMangoldt`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 727

number_theory.von_mangoldt ⟷ Mathlib.NumberTheory.VonMangoldt

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 727

`number_theory.von_mangoldt` ⟷ `Mathlib.NumberTheory.VonMangoldt`