整权与半整权模形式（英文版）
出版时间：2012年版
内容简介
模形式理论是数论的一个十分重要的分支，它在数学和物理学的许多领域有十分重要的应用。《整权与半整权模形式（精）》由XueliWang、DingyiPei所著，本书将全面介绍整权和半整权单变量模形式的基本理论和现代研究成果：低权模形式（主要是低权Eisenstein级数）的构造，整权与半整权模形式之间的联系，模形式在二次型的算术研究中的某些应用。本书的主要特点是同时介绍和研究整权与半整权模形式的理论及其应用。书中既包含了模形式的基本理论，如：模群及其同余子群，Hecke算子等，也包含了许多现代的研究成果，如：整权和半整权模形式的Zeta函数，整权和半整权的Eisenstein级数，Cohen-Eisenstein级数，半整权模形式到整权模形式的Shimura提升，整权和半整权模形式空间上Hecke算子的迹公式，以及模形式理论在二次型的某些算术问题中的应用。
目录
Chapter 1 Theta Functio and Their Traformation FormulaeChapter 2 Eisetein Series 2.1 Eisetein Series with Half Integral Weight 2.2 Eisetein Series with Integral WeightChapter 3 The Modular Group and Its SubgroupsChapter 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-IntegralWeight ReferencesChapter 5 Operato on the Space of Modular Forms 5.1 Hecke Rings 5.2 A Representation of the Hecke Ring on the Space of ModularForms 5.3 Zeta Functio of Modular Forms, Functional Equation,WeilTheorem 5.4 Hecke Operato on the Space of Modular Forms withHalf-Integral Weight ReferencesChapter 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 FormsChapter 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 ReferencesChapter 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 ReferencesChapter 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) ReferencesChapter 10 Intege Represented by Positive Definite Quadratic Forms 10.1 Theta Function of a Positive Definite Quadratic Form andIts Values at Cusp Points 10.2 The Minimal Integer Represented by a Positive DefiniteQuadratic Form 10.3 The Eligible Numbe of a Positive Definite TernaryQuadratic Form ReferencesIndex
