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Modular Forms

  • Toshitsune Miyake

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Toshitsune Miyake
    Pages 1-36
  3. Toshitsune Miyake
    Pages 37-78
  4. Toshitsune Miyake
    Pages 79-95
  5. Toshitsune Miyake
    Pages 96-194
  6. Toshitsune Miyake
    Pages 195-218
  7. Toshitsune Miyake
    Pages 219-267
  8. Toshitsune Miyake
    Pages 268-293
  9. Back Matter
    Pages 295-338

About this book

Introduction

For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who has revised it substantially for the English edition. It sets out to provide the reader with the basic knowledge of elliptic modular forms necessary to understand the recent developments in number theory. The first part gives the general theory of modular groups, modular forms and Hecke operators, with emphasis on the Hecke-Weil theory of the relation between modular forms and Dirichlet series. The second part is on the unit groups of quaternion algebras, which are seldom dealt with in books. The so-called Eichler-Selberg trace formula of Hecke operators follows next and the explicit computable formula is given. In the last chapter, Eisenstein series with parameter are discussed following the recent work of Shimura: Eisenstein series are likely to play a very important role in the future progress of number theory, and this chapter provides a good introduction to the topic.

Keywords

Eichler-Selberg trace formula Eisenstein series Hecke operator Hecke-Weil theory Primitive form number theory

Authors and affiliations

  • Toshitsune Miyake
    • 1
  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-29593-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-22188-4
  • Online ISBN 978-3-540-29593-8
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site