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I am taking a course on Analytic Number Theory. For that, as a pre-requisite, complex analysis is needed. Can anyone give me a video lecture series to start complex analysis? I need to know about holomorphic functions and their singularities, and contour integration(Mentioned by my course instructor).

If anyone can refer a good book, then also it will be helpful.

J. W. Tanner
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roydiptajit
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  • A good source for videos is youtube. –  Nov 17 '20 at 15:55
  • https://www.youtube.com/playlist?list=PLHjOMouVJ7UXj9RqccYzktlz9DQdE6l66 Check this link out. –  Nov 17 '20 at 16:04
  • Books: https://math.stackexchange.com/questions/30749/what-is-a-good-complex-analysis-textbook-barring-ahlforss, https://math.stackexchange.com/questions/160132/complex-analysis-book – Hans Lundmark Nov 17 '20 at 16:04

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I think a good way to go about learning complex analysis would be to use this book: https://www.fing.edu.uy/~cerminar/Complex_Analysis.pdf

along with these lectures:

https://www.youtube.com/watch?v=bfrIk13rAJ4&list=PL71JUoXcec_mmLm9psjMKo1FYBXS9WHb7&ab_channel=StevenMiller

Hope this helps!

Samael Manasseh
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You may take a look at Complex Analysis written by Bak and Newman. The short proof of the prime number theorem that Newman discovered in 1980 is replicated in this book.

You may also try Ash and Novinger's Complex Variables (this link is legitimate; the book is freely available from Prof. Ash's website; a very cheap printed version was published by Dover Publications). It contains Newman's proof of the prime number theorem as well as Dixon's short proof of Cauchy's theorem, the key theorem in every undergraduate course on complex analysis.

Ramen Nii-chan
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