Topics in classical automorphic forms / Henryk Iwaniec.

Format:

Book

Author/Creator:

Iwaniec, Henryk, author.

Series:

Graduate studies in mathematics ; v. 17.

Graduate studies in mathematics ; volume 17

Language:

English

Subjects (All):

Automorphic forms.

Physical Description:

1 online resource (281 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1997]

Language Note:

English

Summary:

This volume discusses various perspectives of the theory of automorphic forms drawn from the author's notes from a Rutgers University graduate course. In addition to detailed and often nonstandard treatment of familiar theoretical topics, the author also gives special attention to such subjects as theta- functions and representatives by quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR

Contents:

""Cover""; ""Title""; ""Copyright""; ""Contents""; ""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""

""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 T[sub(n)]""; ""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-funetion""; ""8.2. Elliptic curves E[sub(r)]""; ""8.3. Computing λ(p)""; ""8.4. A Hecke Grossencharacter""; ""8.5. A theta series""; ""8.6. The automorphy of Æ?""; ""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""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 255-256) and index.

Description based on print version record.

ISBN:

1-4704-2074-0