Spectral methods of automorphic forms / Henryk Iwaniec.

Format:

Book

Author/Creator:

Iwaniec, Henryk, author.

Series:

Graduate studies in mathematics ; v. 53.

Graduate studies in mathematics, 1065-7339 ; volume 53

Language:

English

Subjects (All):

Automorphic functions.

Automorphic forms.

Spectral theory (Mathematics).

Physical Description:

1 online resource (234 p.)

Edition:

Second edition.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2002]

Language Note:

English

Summary:

Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style.The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references.Iwaniec treats the spectral theory of automorphic forms as the study of the space of L^2 functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues.Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.

Contents:

""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Preface to AMS edition""; ""Introduction""; ""Harmonic analysis on the Euclidean plane""; ""Harmonic analysis on the hyperbolic plane""; ""Fuchsian groups""; ""Automorphic forms""; ""The spectral theorem. Discrete part""; ""The automorphic Green function""; ""Analytic continuation of the Eisenstein series""; ""The spectral theorem. Continuous part""; ""Estimates for the Fourier coefficients of Maass forms""; ""Spectral theory of Kloosterman sums""; ""The trace formula""; ""The distribution of eigenvalues""

""Hyperbolic lattice-point problems""""Spectral bounds for cusp forms""; ""Classical analysis""; ""Special functions""; ""References""; ""Subject index""; ""Notation index""; ""Back Cover""

Notes:

First edition published in Revista matemática iberoamericana in 1995.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-1798-7

OCLC:

922965098