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Titlebook: Complex Analysis; Rolf Busam,Eberhard Freitag Textbook 2009Latest edition Springer-Verlag Berlin Heidelberg 2009 Complex Analysis.Elliptic

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书目名称Complex Analysis
编辑Rolf Busam,Eberhard Freitag
视频video
概述All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed.Provides a more in-depth introduction t
丛书名称Universitext
图书封面Titlebook: Complex Analysis;  Rolf Busam,Eberhard Freitag Textbook 2009Latest edition Springer-Verlag Berlin Heidelberg 2009 Complex Analysis.Elliptic
描述.The idea of this book is to give an extensive description of the classical complex analysis, here ‘‘classical‘‘ means roughly that sheaf theoretical and cohomological methods are omitted....The first four chapters cover the essential core of complex analysis presenting their fundamental results. After this standard material, the authors step forward to elliptic functions and to elliptic modular functions including a taste of all most beautiful results of this field. The book is rounded by applications to analytic number theory including distinguished pearls of this fascinating subject as for instance the Prime Number Theorem. Great importance is attached to completeness, all needed notions are developed, only minimal prerequisites (elementary facts of calculus and algebra) are required....More than 400 exercises including hints for solutions and many figures make this an attractive, indispensable book for students who would like to have a sound introduction to classical complex analysis....For the second edition the authors have revised the text carefully..
出版日期Textbook 2009Latest edition
关键词Complex Analysis; Elliptic Functions; Elliptic Modular Forms; Minimum; Modular form; Residue theorem; calc
版次2
doihttps://doi.org/10.1007/978-3-540-93983-2
isbn_softcover978-3-540-93982-5
isbn_ebook978-3-540-93983-2Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag Berlin Heidelberg 2009
The information of publication is updating

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Analytic Number Theory,f four or eight squares by purely function theoretical means..Starting with the second section, we will be concerned with Dirichlet series, including the Riemann .-function. There is a strong connection between modular forms and Dirichlet series (Sect. VII.3). We prove Hecke’s Theorem, claiming a on
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In memoriam Manfred Opp de Hiptelliptic functions. This motivated K. WEIERSTRASS to turn the tables. In his lectures in the winter term 1862/1863 he gave a purely function theoretical introduction to the theory of elliptic functions. In the center of this new setup, there is a special function, the ℘-function. It satisfies a diff
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Introduction,ntroduced formal expressions as for instance ., in order to express solutions of quadratic and cubic equations. Around 1560 R. BOMBELLI computed systematically using such expressions and found 4 as a solution of the equation . in the disguised form.Also in the work of G.W. LEIBNIZ (1675) one can fin
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Differential Calculus in the Complex Plane C,ntered the system C of complex numbers. The same assumption is made for topological notions in C (. etc.). For this reason we shall not dwell on these matters. In Sect. I.4 we introduce the notion of .. One can begin reading directly with this section if one is already sufficiently familiar with the
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Integral Calculus in the Complex Plane C,such that ..In general, one may ask: Which functions . open, have a primitive? Recall that in the real case any . function ., has a primitive, namely, for example the integral.Whether one uses the notion of a RIEMANN integral or the integral for regulated functions is irrelevant in this connection.
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