中國農(nóng)產(chǎn)品現(xiàn)代物流發(fā)展戰(zhàn)略研究

內(nèi)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.

作者簡介

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

書籍目錄

Chapter 1 Theta Functions and Their Transformation FormulaeChapter 2 Eisenstein Series2.1 Eisenstein Series with Half Integral Weight2.2 Eisenstein Series with Integral WeightChapter 3 The Modular Group and Its SubgroupsChapter 4 Modular Forms with Integral Weight or Half-integral Weight4.1 Dimension Formula for Modular Forms with Integral Weight4.2 Dimension Formula for Modular Forms with Half-Integral WeightReferencesChapter 5 Operators on the Space of Modular Forms5.1 Hecke Rings5.2 A Representation of the Hecke Ring on the Space of Modular Forms5.3 Zeta Functions of Modular Forms,Functional Equation,Weil Theorem5.4 Hecke Operators on the Space of Modular Forms with Half-Integral WeightReferencesChapter 6 New Forms and Old Forms6.1 New Forms with Integral Weight6.2 New Forms with Half Integral Weight6.3 Dimension Formulae for the Spaces of New FormsChapter 7 Construction of Eisenstein Series7.1 Construction of Eisenstein Series with Weight≥5/27.2 Construction of Eisenstein Series with Weight 1/27.3 Construction of Eisenstein Series with Weight 3/27.4 Construction of Cohen-Eisenstein Series7.5 Construction of Eisenstein Series with Integral WeightReferencesChapter 8 Weil Representation and Shimura Lifting8.1 Weil Representation8.2 Shimura Lifting for Cusp Forms8.3 Shimura Lifting of Eisenstein Spaces8.4 A Congruence Relation between Some Modular FormsReferencesChapter 9 Trace Formula9.1 Eichler-Selberg Trace Formula on SL2(Z)9.2 Eichler-Selberg Trace Formula on Fuchsian Groups9.3 Trace Formula on the Space Sk+1/2(N,χ)ReferencesChapter 10 Integers Represented by Positive Definite Quadratic Forms10.1 Theta Function of a Positive Definite Quadratic Form and Its Values at Cusp Points10.2 The Minimal Integer Represented by a Positive Definite Quadratic Form10.3 The Eligible Numbers of a Positive Definite Ternary Quadratic FormReferencesIndex

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