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Titlebook: Eta Products and Theta Series Identities; Günter K?hler Book 2011 Springer-Verlag Berlin Heidelberg 2011 11-02, 11F20, 11F27, 11R11.Eisens

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發(fā)表于 2025-3-21 17:46:04 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Eta Products and Theta Series Identities
編輯Günter K?hler
視頻videohttp://file.papertrans.cn/316/315833/315833.mp4
概述This monograph brings to the public the large number of identities which were found during the past 20 years.The majority of these identities is new and has not been published elsewhere.Presents more
叢書(shū)名稱Springer Monographs in Mathematics
圖書(shū)封面Titlebook: Eta Products and Theta Series Identities; Günter K?hler Book 2011 Springer-Verlag Berlin Heidelberg 2011 11-02, 11F20, 11F27, 11R11.Eisens
描述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 of the book. 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.
出版日期Book 2011
關(guān)鍵詞11-02, 11F20, 11F27, 11R11; Eisenstein series; Hecke theta series; eta products; modular forms (one vari
版次1
doihttps://doi.org/10.1007/978-3-642-16152-0
isbn_softcover978-3-642-26629-4
isbn_ebook978-3-642-16152-0Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightSpringer-Verlag Berlin Heidelberg 2011
The information of publication is updating

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沙發(fā)
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板凳
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Liang See Tan,Keith Chiu Kian Tantions in some textbooks; we mention (Miyake in Modular Forms, Springer, Berlin, .), pp. 90–95, 182–185, (Neukirch in Algebraische Zahlentheorie, Springer, Berlin, .. English Translation: Algebraic Number Theory, Springer, Berlin, 1999), pp. 491–514. Here we will reproduce relevant definitions and results, but we will not give proofs.
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Groups of Coprime Residues in Quadratic Fieldsecifying its values on the generators. In almost all of the examples in Part?II we will define characters in this way. For this purpose we need to know a decomposition of the groups into direct factors, and we need to know generators of the factors.
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The prime level ,=3oduct of level . and weight 1 for primes .≥5. The eta product .(.).(3.) is identified with a Hecke theta series for .; the result (11.2) is known from (Dummit et al. in Finite Groups—Coming of Age. Contemp.?Math.?45, 89–98, .), (K?hler in Math.?Z.?197, 69–96, .).
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