contour integrals

Stream: maths

[Junyan Xu]

Re: the difficult contour in the last page of the slides: I think it's the same as Figure 2.7 in Apostol. According to Wenda Li, they have formalized four chapters of the book, presumably including Chapter 2. In fact page 26 onwards of these slides is specifically about this type of contours. The finite-dimensionality proof is in Chapter 6 though.

[David Loeffler]

Junyan Xu said:

Re: the difficult contour in the last page of the slides: I think it's the same as Figure 2.7 in Apostol. According to Wenda Li, they have formalized four chapters of the book, presumably including Chapter 2. In fact page 26 onwards of these slides is specifically about this type of contours. The finite-dimensionality proof is in Chapter 6 though.

Wow, that's awesome. I suspected that dealing with poles on the boundary would considerably complicate the proof, and it seems that I wasn't wrong – it looks like they had to invent some really genuinely new mathematics to handle it. @Chris Birkbeck have you seen this?

[Alex Kontorovich]

I wonder if it would be useful to organize a little informal zoom mini-workshop to swap tricks specific to this kind of stuff? A lot of people seem to be developing really novel approaches (as you say, "genuinely new mathematics") for dealing with complex analysis and applications...

[Chris Birkbeck]

David Loeffler said:

Junyan Xu said:

Re: the difficult contour in the last page of the slides: I think it's the same as Figure 2.7 in Apostol. According to Wenda Li, they have formalized four chapters of the book, presumably including Chapter 2. In fact page 26 onwards of these slides is specifically about this type of contours. The finite-dimensionality proof is in Chapter 6 though.

Wow, that's awesome. I suspected that dealing with poles on the boundary would considerably complicate the proof, and it seems that I wasn't wrong – it looks like they had to invent some really genuinely new mathematics to handle it. Chris Birkbeck have you seen this?

Yes! I gave a talk last year at Cambridge and Wenda showed me this (and lots of other interesting things!). I've been meaning to find the time/collaborator/student to work on this as I really want it for the finite dimensionality of spaces of modular forms. I haven't watched the talk yet, but I'm guessing this is what the question was about. I'm also interested to know where we are with meromorphic functions (but perhaps on another stream).

[Notification Bot]

6 messages were moved here from #announce > David Loeffler lecture in the Rutgers lean seminar by Johan Commelin.

[Johan Commelin]

@David Loeffler @Alex Kontorovich @Junyan Xu I moved the messages about contour integrals out of the #announce stream into this separate thread. (#announce is followed by many people, so we try to keep it low traffic)