Modular Forms With Integral And Half-Integral Weights

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 Forms
5.3 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
7.3 Construction of Eisenstein Series with Weight 3/2
7.4 Construction of Cohen-Eisenstein Series
7.5 Construction of Eisenstein Series with Integral Weight
References
Chapter 8 Weil Representation and Shimura Lifting
8.1 Weil Representation
8.2 Shimura Lifting for Cusp Forms
8.3 Shimura Lifting of Eisenstein 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,χ)
References
Chapter 10 Integers 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 Numbers of a Positive Definite Ternary Quadratic Form
References