Universitext

Complex Analysis 2

Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions

Authors: Freitag, Eberhard

  • 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 to the subject than other existing books in this area
  • Many exercises including hints for solutions are included
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eBook $69.99
price for USA
  • ISBN 978-3-642-20554-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-642-20553-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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  • Rental duration: 1 or 6 month
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About this Textbook

The book provides a complete presentation of complex analysis, starting with the theory of Riemann surfaces, including uniformization theory and a detailed treatment of the theory of compact Riemann surfaces, the Riemann-Roch theorem, Abel's theorem and Jacobi's inversion theorem. This motivates a short introduction into the theory of several complex variables, followed by the theory of Abelian functions up to the theta theorem. The last part of the book provides an introduction into the theory of higher modular functions.

About the authors

Prof. Dr. Eberhard Freitag, Universität Heidelberg, Mathematisches Institut

Reviews

From the reviews:

“The book under review is the second volume of the textbook Complex analysis, consisting of 8 chapters. It provides an approach to the theory of Riemann surfaces from complex analysis. … The book is self-contained and, moreover, some notions which might be unfamiliar for the reader are explained in appendices of chapters. … this book is an excellent textbook on Riemann surfaces, especially for graduate students who have taken the first course of complex analysis.” (Hiroshige Shiga, Mathematical Reviews, Issue 2012 f)

“The book under review is largely self-contained, pleasantly down-to-earth, remarkably versatile, and highly educating simultaneously. No doubt, this fine textbook provides an excellent source for the further study of more advanced and topical themes in the theory of Riemann surfaces, their Jacobians and moduli spaces, and in the general theory of complex Abelian varieties and modular forms likewise. It is very welcome that the English translation of the German original has been made available so quickly!” (Werner Kleinert, Zentralblatt MATH, Vol. 1234, 2012)

“The author provides a (very brief) introduction to fundamental notions of topology, but develops fully the theory of surfaces and covering spaces he needs. … the book includes a proof of the classification of compact orientable surfaces by their genus. … this one is definitely a graduate text. … There is a lot of mathematics in this book, presented efficiently and well. … It is a book I am glad to have, and that I will certainly refer to in the future.” (Fernando Q. Gouvêa, The Mathematical Association of America, May, 2012)


Table of contents (8 chapters)

Buy this book

eBook $69.99
price for USA
  • ISBN 978-3-642-20554-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-642-20553-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Complex Analysis 2
Book Subtitle
Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-20554-5
DOI
10.1007/978-3-642-20554-5
Softcover ISBN
978-3-642-20553-8
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XIII, 506
Number of Illustrations and Tables
51 b/w illustrations
Topics