- 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- The majority of these identities are new and unpublished elsewhere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
Buy this book
- About this book
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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
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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)
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Dedekind’s Eta Function and Modular Forms
Pages 3-30
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Eta Products
Pages 31-37
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Eta Products and Lattice Points in Simplices
Pages 39-54
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An Algorithm for Listing Lattice Points in a Simplex
Pages 55-65
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Theta Series with Hecke Character
Pages 67-79
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Table of contents (31 chapters)
- Download Preface 1 PDF (112.8 KB)
- Download Sample pages 2 PDF (310.6 KB)
- Download Table of contents PDF (151.7 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Eta Products and Theta Series Identities
- Authors
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- Günter Köhler
- 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
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