Decision to be made on (2 \pi i) factors

Stream: PrimeNumberTheorem+

[Alex Kontorovich]

We're getting to the point where those $2\pi i$ factors are going to start appearing everywhere, since we're actually trying to evaluate residues. Any objections to rolling them into the definition of VerticalIntegral, so they don't need to be explicated every time? Perhaps RectangleIntegral should also have a $1/(2\pi i)$ in front, since we'll need to convert between the two regularly? Any suggestions, one way or another? (@Terence Tao)

[Terence Tao]

I don't think it will make too much difference, but if one were to put in the 2 pi i factor I would change the name slightly. One possibility is to make an abbrev such as VerticalIntegral' that is simply VerticalIntegral divided by 2 pi i, then people can use whichever form of the integral they wish.

In the Wiener-Ikehara section the 2 pi factor is moved to the exponent in order to be compatible with the Matlhlib Fourier transform, but I think this isn't too hard to deal with. Again one could address this by defining a variant e' of the character e that doesn't have the 2 pi factor (i.e., $e'(x) = e^{ix}$ and $e(x) =e^{2\pi i x}$) if desired, but I don't think this is going to be the main difficulty in the formalization of this section in any event.

[Alex Kontorovich]

Ok good idea, I'll keep both, so we have the flexibility to use either as convenient...