دانلود کتاب Modular Forms with Integral and Half-Integral Weights

Title Page; Copyright Page; Preface; Table of Contents; Chapter 1 Theta Functions and Their Transformation Formulae; Chapter 2 Eisenstein Series; 2.1 Eisenstein Series with Half Integral Weight; 2.2 Eisenstein 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 Dimension Formula for Modular Forms with Integral Weight; 4.2 Dimension Formula for Modular Forms with Half-Integral Weight; References; Chapter 5 Operators on the Space of Modular Forms; 5.1 Hecke Rings. 5.2 A Representation of the Hecke Ring on the Space of Modular Forms5.3 Zeta Functions of Modular Forms, Functional Equation, Weil Theorem; 5.4 Hecke Operators 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 Dimension Formulae for the Spaces of New Forms; Chapter 7 Construction of Eisenstein Series; 7.1 Construction of Eisenstein Series with Weight 5/2; 7.2 Construction of Eisenstein Series with Weight 1/2. Chapter 10 Integers Represented by Positive Definite Quadratic Forms10.1 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 Numbers of a Positive Definite Ternary Quadratic Form; References; Index