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 Well 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,x)
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
Index