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Author Wang, Xueli, 1963-
Title Modular forms with integral and half-integral weights / Xueli Wang, Dingyi Pei.
Imprint Beijing : Science Press ; Heidelberg ; London : Springer, 2012.

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Author Wang, Xueli, 1963-
Subject Forms, Modular.
Eisenstein series.
Mathematics.
Alt Name Pei, Dingyi.
Description 1 online resource (x, 432 pages) : illustrations
polychrome rdacc
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.
Bibliography Note Includes bibliographical references and index.
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 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.
Note Print version record.
ISBN 9783642293023 (electronic bk.)
3642293026 (electronic bk.)
9783642293016
3642293018
9787030330796
ISBN/ISSN 10.1007/978-3-642-29302-3
OCLC # 828664034
Additional Format Print version: Wang, Xueli, 1963- Modular forms with integral and half-integral weights. Beijing : Science Press ; Heidelberg ; London : Springer, 2012 9783642293016 (OCoLC)809564569


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