Geometric Theory of Functions of a Complex Variable (Translations of Mathematical Monographs)
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Get 'em. Whittaker and Watson. Hardy, Wright, and Hardy and Wright learned complex analysis from it. Complex variables: An introduction , by Carlos A. Berenstein and Roger Gay Springer, This is a self-contained, very accessible, comprehensive, and masterfully written textbook that I do find very suitable for the serious self-taught possessing the rare mathematical maturity, and being in command of a quite modest but non-negligible background.
So for instance, once you're going to tackle Cauchy's integral theorem, you'll be fully equipped to prove it in its full generality, and without the typical "hand-weaving" most texts rely on and hide behind. A following up by the same authors is Complex analysis and special topics in harmonic analysis Springer, I think Using the Mathematics Literature may be helpful to answer your question.
Boas is really nice, and suitable for self study because it has about 60 pages of solutions to the texts problems. You might like Functions of a Complex Variable by E. It is slightly dated, but you can't argue with the price!
I personally think this is a wonderful book. That's a really excellent textbook! Trust me! Only covers the basics, but explains them in a crystal clear style. I've taught a few times from Churchill's book, and used it as an undergrad. I'm liking it less all the time. I used this in the beginning grad course in complex, along with Hille's "Analytic Function Theory," which I liked very much. Zill" and for little advanced case i would like to refer " Complex Analysis by Dennis G.
Zill and Patrick Shanahan". Hope this helps! Lots of good recommendations here-but for self study,you can't beat Complex analysis by Theodore W. It's highly geometric, has very few prerequisites and reaches very near the boundaries of research by the end. This has plenty of solved and unsolved exercises ranging from the basics on complex numbers, to special functions and conformal mappings. This has a note on the zeta function. It covers classic topics, such as the Schwarz lemma and Riemann mapping theorem, and moves onto topics in harmonic analysis and abstract algebra.
This book contains a detailed analysis of complex analysis and number theory especially the zeta function. Topics covered include complex integration in number theory, the Zeta function and L-functions.
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Geometric Theory Functions Complex Variable
Ask Question. Asked 8 years, 5 months ago. Active 3 months ago. Viewed 87k times. Number Theory 2 Kazuya Kato.
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Introduction to Complex Analysis Junjiro Noguchi. Introduction to Analytic Number Theory A. Rating details. Book ratings by Goodreads. Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book.
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Close X. The appearance of elliptic integrals finds a natural explanation: they arise because a certain associated covering surface of the Riemann sphere is a torus. Unable to display preview. Download preview PDF.
Graham , Varolin : Bloch constants in one and several variables.
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