Springer Monographs in Mathematics

Eta Products and Theta Series Identities

Authors: Köhler, Günter

  • Presents to the public the large number of identities which were found during the past 20 years
  • The majority of these identities are new and unpublished elsewhere
  • Includes more than a hundred examples for the coincidence of theta series of weight 1 on three distinct quadratic fields
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eBook 74,96 €
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  • ISBN 978-3-642-16152-0
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Hardcover 93,55 €
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  • ISBN 978-3-642-16151-3
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  • Usually dispatched within 3 to 5 business days.
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Softcover 93,55 €
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  • ISBN 978-3-642-26629-4
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About this book

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.

Reviews

From the reviews:

“This monograph serves as a leading reference on the theory of eta products and theta series identities. The systematic approach to the theory of modular forms in general and eta products in particular makes it a reader-friendly monograph for those who have basic knowledge about the theory.” (Wissam Raji, Mathematical Reviews, Issue 2012 a)

“In the book under review mainly a highly interesting special class of theta functions is investigated, the class of Hecke theta series for quadratic number fields. … Most of the identities in the later sections of this monograph are supposed to be new. Clearly this is a most valuable addition to the literature on modular forms, and the modular forms people must be most grateful to the author for his fine achievement.” (Jürgen Elstrodt, Zentralblatt MATH, Vol. 1222, 2011)


Table of contents (31 chapters)

  • Dedekind’s Eta Function and Modular Forms

    Köhler, Günter

    Pages 3-30

    Preview Buy Chapter 30,19 €
  • Eta Products

    Köhler, Günter

    Pages 31-37

    Preview Buy Chapter 30,19 €
  • Eta Products and Lattice Points in Simplices

    Köhler, Günter

    Pages 39-54

    Preview Buy Chapter 30,19 €
  • An Algorithm for Listing Lattice Points in a Simplex

    Köhler, Günter

    Pages 55-65

    Preview Buy Chapter 30,19 €
  • Theta Series with Hecke Character

    Köhler, Günter

    Pages 67-79

    Preview Buy Chapter 30,19 €

Buy this book

eBook 74,96 €
price for Spain (gross)
  • ISBN 978-3-642-16152-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 93,55 €
price for Spain (gross)
  • ISBN 978-3-642-16151-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 93,55 €
price for Spain (gross)
  • ISBN 978-3-642-26629-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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
Eta Products and Theta Series Identities
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-16152-0
DOI
10.1007/978-3-642-16152-0
Hardcover ISBN
978-3-642-16151-3
Softcover ISBN
978-3-642-26629-4
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XXII, 622
Topics