The Selberg-Arthur Trace Formula: Based on Lectures by James Arthur / Edition 1

by Salahoddin Shokranian

Overview

This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks

Product Details

ISBN-13:	9783540550211
Publisher:	Springer Berlin Heidelberg
Publication date:	03/17/1992
Series:	Lecture Notes in Mathematics , #1503
Edition description:	1992
Pages:	99
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

Contents: Number Theory and Automorphic Representations: Some problems in classical number theory. Modular forms and automorphic representations.- Selberg's Trace Formula: Historical Remarks. Orbital integrals and Selberg's trace formula. Three examples. A necessary condition. Generalizations and applications.- Kernel Functions and the Convergence Theorem: Preliminaries on GL(r). Combinatorics and reduction theory. The convergence theorem.- The Adélic Theory: Basic facts.- The Geometric Theory: The JTO(f) and JT(f) distributions. A geometric I-function. The weight functions.- The Geometric Expansion of the Trace Formula: Weighted orbital integrals. The unipotent distribution.- The Spectral Theory: A review of the Eisenstein series. Cusp forms, truncation, the trace formula.- The Invariant Trace Formula and Its Applications: The in- variant trace formula for GL(r). Applications and remarks.- Bibliography.- Subject Index.