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" Modular Forms with Integral and Half-Integral Weights "
by Xueli Wang, Dingyi Pei.
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BL
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577964
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b407183
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| Main Entry
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Wang, Xueli.
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| Title & Author
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Modular Forms with Integral and Half-Integral Weights\ by Xueli Wang, Dingyi Pei.
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| Publication Statement
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Berlin, Heidelberg :: Springer Berlin Heidelberg :: Imprint: Springer,, 2012.
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Approx. 400 p. 3 illus.: digital.
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| ISBN
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9783642293023
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| Contents
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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.
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| Abstract
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"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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Mathematics.
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Geometry, Algebraic.
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Functions of complex variables.
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Number theory.
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Mathematics.
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Number theory.
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Geometry, Algebraic.
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Functions of complex variables.
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Pei, Dingyi.
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SpringerLink (Online service)
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