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Modular forms with integral and half-integral weights

Autor: Xueli Wang; Dingyi Pei
Editora: Beijing : Science Press ; Heidelberg ; London : Springer, ©2012.
Edição/Formato   e-book : Documento : InglêsVer todas as edições e formatos
Base de Dados:WorldCat
Resumo:
"Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater  Ler mais...
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Gênero/Forma: Electronic books
Formato Físico Adicional: Print version:
Wang, Xueli, 1963-
Modular forms with integral and half-integral weights.
Beijing : Science Press ; Heidelberg ; London : Springer, c2012
(OCoLC)809564569
Tipo de Material: Documento, Recurso Internet
Tipo de Documento: Recurso Internet, Arquivo de Computador
Todos os Autores / Contribuintes: Xueli Wang; Dingyi Pei
ISBN: 9783642293023 3642293026
Número OCLC: 828664034
Descrição: 1 online resource (x, 432 p.) : ill.
Conteúdos: Theta Functions and Their Transformation Formulae --
Eisenstein Series --
The Modular Group and Its Subgroups --
Modular Forms with Integral Weight or Half-integral Weight --
Operators on the Space of Modular Forms --
New Forms and Old Forms --
Construction of Eisenstein Series --
Weil Representation and Shimura Lifting --
Trace Formula --
Integers Represented by Positive Definite Quadratic Forms.
Responsabilidade: Xueli Wang, Dingyi Pei.
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Resumo:

Taking the theory of Eisenstein series as its core theme, this volume focuses on the fundamental principles of modular forms of one variable. With analysis of half-integral as well as integral  Ler mais...

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From the reviews: "The reader will find a thorough introduction to many central themes in the theory of modular forms of integral and half-integral weight in one variable. ... This monograph is a Ler mais...

 
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schema:description""Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that the conclusion holds true for weight 3/2 by explicitly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. The book provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers and practitioners in modular forms of mathematics. Dr. Xueli Wang is a Professor at South China Normal University, China. Dingyi Pei is a Professor at Guangzhou University, China."
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