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Eta Products and Theta Series Identities

  • Günter Köhler

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

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Theoretical Background

    1. Front Matter
      Pages 1-1
    2. Günter Köhler
      Pages 3-30
    3. Günter Köhler
      Pages 31-37
    4. Günter Köhler
      Pages 39-54
    5. Günter Köhler
      Pages 67-79
  3. Examples

    1. Front Matter
      Pages 97-97
    2. Günter Köhler
      Pages 99-112
    3. Günter Köhler
      Pages 119-131
    4. Günter Köhler
      Pages 133-153
    5. Günter Köhler
      Pages 155-171
    6. Günter Köhler
      Pages 173-186
    7. Günter Köhler
      Pages 187-214
    8. Günter Köhler
      Pages 215-221
    9. Günter Köhler
      Pages 223-250
    10. Günter Köhler
      Pages 251-265
    11. Günter Köhler
      Pages 267-290
    12. Günter Köhler
      Pages 291-304
    13. Günter Köhler
      Pages 305-318
    14. Günter Köhler
      Pages 319-346
    15. Günter Köhler
      Pages 347-368
    16. Günter Köhler
      Pages 369-396
    17. Günter Köhler
      Pages 397-425
    18. Günter Köhler
      Pages 427-454
    19. Günter Köhler
      Pages 455-484
    20. Günter Köhler
      Pages 513-525
    21. Günter Köhler
      Pages 527-545
    22. Günter Köhler
      Pages 547-558
    23. Günter Köhler
      Pages 571-591
  4. Back Matter
    Pages 593-621

About this book

Introduction

This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic number fields, and with Eisenstein series. The author brings to the public the large number of identities that have been discovered over the past 20 years, the majority of which have not been published elsewhere. The book will be of interest to graduate students and scholars in the field of number theory and, in particular, modular forms. It is not an introductory text in this field. Nevertheless, some theoretical background material is presented that is important for understanding the examples in Part II. In Part I relevant definitions and essential theorems -- such as a complete proof of the structure theorems for coprime residue class groups in quadratic number fields that are not easily accessible in the literature -- are provided. Another example is a thorough description of an algorithm for listing all eta products of given weight and level, together with proofs of some results on the bijection between these eta products and lattice simplices.

Keywords

11-02, 11F20, 11F27, 11R11 Eisenstein series Hecke theta series eta products modular forms (one variable) number theory quadratic number fields sums of squares

Authors and affiliations

  • Günter Köhler
    • 1
  1. 1.Institute of MathematicsUniversity of WürzburgWürzburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-16152-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-16151-3
  • Online ISBN 978-3-642-16152-0
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site