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Modular forms with integral and half-integral weights

Author: Xueli Wang; Dingyi Pei
Publisher: Beijing : Science Press ; Heidelberg ; London : Springer, ©2012.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
"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  Read more...
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Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Xueli Wang; Dingyi Pei
ISBN: 3642293026 9783642293023
OCLC Number: 832593610
Notes: Titre de l'écran-titre (visionné le 12 mars 2013).
Description: 1 online resource (1 texte électronique (x, 432 p.)) ill., fichiers PDF.
Contents: 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.
Responsibility: Xueli Wang, Dingyi Pei.
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Abstract:

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  Read more...

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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 Read more...

 
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schema:description"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."
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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