《经典自守形式专题(英文版)(精)》是基于作者亨里克·伊万涅茨于1994年秋和1995年春在Rutgers大学的研究生课程的讲义发展而来。主要目的是向读者提供多种视角来了解自守形式理论。除了对理论中熟知的专题做详细且常常是非标准的阐述外，还特别关注诸如θ－函数以及二次型表示这些课题。本书的读者包括数论和相关的代数几何方向的研究生和数学家。

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
8.1. The Hasse-Weil L-function
8.2. Elliptic curves Er
8.3. Computing λ(p)
8.4. A Hecke Grossencharacter
8.5. A theta series
8.6. The automorphy of f
Chapter 9. Spherical Functions
9.1. Positive definite quadratic forms
9.2. Space spherical functions
9.3. The spherical functions reconsidered
9.4. Harmonic analysis on the sphere
Chapter 10. Theta Functions
10.1. Introduction
10.2. An inversion formula
10.3. The congruent theta functions
10.4. The automorphy of theta functions
10.5. The standard theta function
Chapter 11. Representations by Quadratic Forms
11.1. Introduction
11.2. Siegel's mass formula
11.3. Representations by Eisenstein series and cusp forms
11.4. The circle method after Kloosterman
11.5. The singular series
11.6. Equidistribution of integral points on ellipsoids
Chapter 12. Automorphic Forms Associated with Number Fields
12.1. Automorphic forms attached to Dirichlet L-functions
12.2. Hecke L-functions with Grossencharacters
12.3. Automorphic forms associated with quadratic fields
12.4. Class group L-functions reconsidered
12.5. L-functions for genus characters
12.6. Automorphic forms of weight one
Chapter 13. Convolution L-functions
13.1. Introduction
13.2. Rankin-Selberg integrals
13.3. Selberg's theory of Eisenstein series
13.4. Statement of general results
13.5. The scattering matrix for Γ0(N)
13.6. Functional equations for the convolution L-functions
13.7. Metaplectic Eisenstein series
13.8. Symmetric power L-functions
Bibliography
Index