00000cmm a22000003a 4500 UP-99796217611255023 Buklod 20250205101630.0 m go j cr |nu|||auu|a 250205s2011 gw o j eng d 978-3-642-16152-0 (eBook) (iLib)UPD-00215706118 DMLR rda eng DMLUC QA 345 K64 2011eb Köhler, Günter author. Eta products and theta series identities [electronic resource] Günter Köhler. Heidelberg, Germany Springer Berlin 2011 1 online resource (xxii, 622 pages) text rdacontent computer rdamedia online resource rdacarrier Springer monographs in mathematics 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. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Functions, Theta. Forms, Modular. Number theory. SpringerLink (Online service). Electronic Resource Available for UP System via SpringerLink. https://doi.org/10.1007/978-3-642-16152-0 FO UPD DMLR QA 345 K64 2011eb Electronic Resource