Preface
Chapter 0. Introduction
Chapter 1. The Classical Modular Forms
1.1. Periodic functions
1.2. Elliptic functions
1.3. Modular functions
1.4. The Fourier expansion of Eisenstein series
1.5. The modular group
1.6. The linear space of modular forms
Chapter 2. Automorphic Forms in General
2.1. The hyperbolic plane
2.2. The classification of motions
2.3. Discrete groups -- Fuchsian groups
2.4. Congruence groups
2.5. Double coset decomposition
2.6. Multiplier systems
2.7. Automorphic forms
2.8. The eta-function and the theta-function
Chapter 3. The Eisenstein and the Poincare Series
3.1. General Poincare series
3.2. Fourier expansion of Poincare series
3.3. The Hilbert space of cusp forms
Chapter 4. Kloosterman Sums
4.1. General Kloosterman sums
4.2. Kloosterman sums for congruence groups
4.3. The classical Kloosterman sums
4.4. Power-moments of Kloosterman sums
4.5. Sums of Kloosterman sums
4.6. The Salie sums
Chapter 5. Bounds for the Fourier Coefficients of Cusp Forms
5.1. General estimates
5.2. Estimates by Kloosterman sums
5.3. Coefficients of cusp forms with theta multiplier
5.4. Linear forms in Fourier coefficients of cusp forms
5.5. Spectral analysis of the diagonal symbol
Chapter 6. Hecke Operators
6.1. Introduction
6.2. Hecke operators Tn
6.3. The Hecke operators on periodic functions
6.4. The Hecke operators for the modular group
6.5. The Hecke operators with a character
6.6. An overview of newforms
6.7. Hecke eigencuspforms for a primitive character
6.8. Final remarks
Chapter 7. Automorphic L-functions
7.1. Introduction
7.2. The Hecke L-functions
7.3. Twisting automorphic forms and L-functions
7.4. Converse theorems
Chapter 8. Cusp Forms Associated with Elliptic Curves
