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＜電子ブック＞
Modular Forms with Integral and Half-Integral Weights / by Xueli Wang, Dingyi Pei

版	1st ed. 2012.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2012
大きさ	X, 432 p. 2 illus : online resource
著者標目	*Wang, Xueli author Pei, Dingyi author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Algebraic geometry LCSH:Functions of complex variables FREE:Number Theory FREE:Algebraic Geometry FREE:Functions of a Complex Variable
一般注記	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 "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 HTTP:URL=https://doi.org/10.1007/978-3-642-29302-3

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