整权与半整权模形式

出版时间：2012-1  出版社：科学出版社  作者：裴定一,王学理  页数：432  字数：400000  
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内容概要

Modular Forms with Integral and Half-Integral Weights focuses on the fundamental theory of modular forms of one variable with intergral 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 cuspforms.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 modem investigatioii methods of modular forms with integral and half-integral weights.It will be of sigruficant interest to researchers and practitioners in modular forms of mathematics.

作者简介

Dr.Xueli Wang is a Professor at South China Normal University,China.Dingyi Pei is a Professor at Guangzhou Univefsity,China.

书籍目录

Chapter 1  Theta Functio and Their Traformation Formulae
Chapter 2  Eisetein Series
    2.1  Eisetein Series with Half Integral Weight
    2.2  Eisetein Series with Integral Weight
Chapter 3  The Modular Group and Its Subgroups
Chapter 4  Modular Forms with Integral Weight or Half-integral
                Weight
    4.1  Dimeion Formula for Modular Forms with Integral Weight
    4.2  Dimeion Formula for Modular Forms with Half-Integral
Weight
    References
Chapter 5  Operato on the Space of Modular Forms
    5.1  Hecke Rings
    5.2  A Representation of the Hecke Ring on the Space of Modular
Forms
    5.3  Zeta Functio of Modular Forms, Functional Equation,Weil
Theorem
    5.4  Hecke Operato on the Space of Modular Forms with
Half-Integral
          Weight
    References
Chapter 6  New Forms and Old Forms
    6.1  New Forms with Integral Weight
    6.2  New Forms with Half Integral Weight
    6.3  Dimeion Formulae for the Spaces of New Forms
Chapter 7  Cotruction of Eisetein Series
    7.1  Cotruction of Eisetein Series with Weight > 5/2
    7.2  Cotruction of Eisetein Series with Weight 1/2
    7.3  Cotruction of Eisetein Series with Weight 3/2
    7.4  Cotruction of Cohen-Eisetein Series
    7.5  Cotruction of Eisetein Series with Integral Weight
    References
Chapter 8  Well Representation and Shimura Lifting
    8.1  Weil Representation
    8.2  Shimura Lifting for Cusp Forms
    8.3  Shimura Lifting of Eisetein Spaces
    8.4  A Congruence Relation between Some Modular Forms
    References
Chapter 9  Trace Formula
    9.1  Eichler-Selberg Trace Formula on SL2(Z)
    9.2  Eichler-Selberg Trace Formula on Fuchsian Groups
    9.3  Trace Formula on the Space Sk+1/2(N,x)
    References
Chapter 10  Intege Represented by Positive Definite Quadratic Forms
    10.1  Theta Function of a Positive Definite Quadratic Form and
Its Values at Cusp Points
    10.2  The Minimal Integer Represented by a Positive Definite
Quadratic Form
    10.3  The Eligible Numbe of a Positive Definite Ternary
Quadratic Form
    References
Index