Explicit Constructions of Automorphic L-Functions / Edition 1

by Stephen Gelbart, Ilya Piatetski-Shapiro, Stephen Rallis

Overview

The goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by Piatetski-Shapiro and Rallis) deals with L-functions for the simple classical groups; the second part (by Gelbart and Piatetski-Shapiro) deals with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory.

Product Details

ISBN-13:	9783540178484
Publisher:	Springer Berlin Heidelberg
Publication date:	06/02/1987
Series:	Lecture Notes in Mathematics , #1254
Edition description:	1987
Pages:	156
Product dimensions:	5.90(w) x 9.10(h) x 0.60(d)

Table of Contents

Contents: L-Functions for the Classical Groups.- L-Functions for G GL(n): Basic Identities and the Euler Product Expansion. The Local Functional Equation.- General Index.- Index of Notation.