🧵 Best "advanced" complex analysis textbooks
Anonymous at Thu, 2 May 2024 19:51:06 UTC No. 16156838
Complex analysis is literal fucking wizardry. I've covered the basics (up to the residue theorem), rec me some texts to learn the more advanced stuff. Hard mode, don't rec
>Ahlfors, Rudin, Lang, Freitag, Remmert, Cartan, Ullrich
ATM looking for a text that covers the Weierstrass factorisation theorem and Runge's theorem well
Anonymous at Thu, 2 May 2024 20:35:23 UTC No. 16156887
If you already know enough, you can just go to the wikipedia page of these theorems and learn from there or check the sources. Also after the basics it is probably more interesting to choose an application and use the methods from complex analysis there, e.g. elliptic functions, modular forms, riemann surfaces, etc.
> Functions of One Complex Variable I + II - John Conway
Anonymous at Thu, 2 May 2024 21:10:16 UTC No. 16156930
>>16156887
>e.g. elliptic functions, modular forms, riemann surfaces
OK, rec some sources then please
Anonymous at Thu, 2 May 2024 21:18:15 UTC No. 16156945
>>16156838
Take a look at the notes for Mat354 and Mat454 as taught by Edward Bierstone.
http://individual.utoronto.ca/rishi
http://individual.utoronto.ca/rishi
Anonymous at Thu, 2 May 2024 21:26:21 UTC No. 16156961
>>16156930
idk what are your interests and knowledge, but if you look up for standard books on these subjects you should find many good sources. For riemann surfaces I'd recommend Forster's Lectures on Riemann Surfaces
Anonymous at Thu, 2 May 2024 21:28:21 UTC No. 16156965
>>16156961
>idk what are your interests and knowledge
I'm interested in applications to number theory. Am pretty well-informed on the algebraic side, starting to get into the analytic side of things, so I'm interested in elliptic functions and modular forms
Anonymous at Thu, 2 May 2024 21:41:35 UTC No. 16156977
>>16156965
ok, good. So the applications I mentioned are really the right ones for you. Apostol's modular functions and dirichlet series is a nice and gentle introduction. You should also check out Dirichlet's L-functions and a proof of the prime number theorem using a tauberian theorem.
Forster's book is also the right one for you.
I usually don't study from following a source, but from looking for a specific topic in multiple sources and professors' lecture notes though