ENGLISH

Eta Products and Theta Series Identities

By Günter Köhler (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2011
ISBN
3642161510, 9783642161513
DOI
10.1007/978-3-642-16152-0
ISSN
1439-7382
Language
english
Format
PDF
Filesize
4 MB (4589959 bytes)
Series
Springer Monographs in Mathematics
Edition
1
Pages
622\644
Orientation
yes
Scanned
no
Time added
2012-03-17 06:00:00
Number Theory; Algebraic Topology

Description

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.

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