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基本説明
An underground classic textbook and a respected source for results, ideas, and references.
Full Description
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 volume was an underground classic, both as a textbook and as a respected source for results, ideas, and references. The book's reputation sparked a growing interest in the mathematical community to bring it back into print. The AMS has answered that call with the publication of this second edition. In the book, Iwaniec treats the spectral theory of automorphic forms as the study of the space $L^2 (H\Gamma)$, where $H$ is the upper half-plane and $\Gamma$ is a discrete subgroup of volume-preserving transformations of $H$.He combines various techniques from analytic number theory. Among the topics discussed are Eisenstein series, estimates for Fourier coefficients of automorphic forms, the theory of Kloosterman sums, the Selberg trace formula, and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 AMS Cole Prize for his fundamental contributions to analytic number theory. Also available from the AMS by H. Iwaniec is ""Topics in Classical Automorphic Forms"", Volume 17 in the ""Graduate Studies in Mathematics"" series. The book is designed for graduate students and researchers working in analytic number theory.
Contents
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.
