Complex Analysis 2

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

  • Eberhard Freitag

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Eberhard Freitag
    Pages 1-53
  3. Eberhard Freitag
    Pages 54-140
  4. Eberhard Freitag
    Pages 141-183
  5. Eberhard Freitag
    Pages 184-299
  6. Eberhard Freitag
    Pages 300-346
  7. Eberhard Freitag
    Pages 347-426
  8. Eberhard Freitag
    Pages 427-482
  9. Eberhard Freitag
    Pages 483-493
  10. Back Matter
    Pages 494-506

About this book

Introduction

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.

Keywords

Abelian Functions Analytic Functions Modular Forms Riemannian Surfaces

Authors and affiliations

  • Eberhard Freitag
    • 1
  1. 1.Inst. MathematikUniversität HeidelbergHeidelbergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-20554-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-20553-8
  • Online ISBN 978-3-642-20554-5
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book