ENGLISH

Explicit Constructions of Automorphic L-Functions

By Stephen Gelbart , Ilya Piatetski-Shapiro , Stephen Rallis

Book information

Publisher
Springer
Year
1987
ISBN
9780387178486, 0387178481
LCC
QA3 .L28 no. 1254,QA246 .L28 no. 1254
Open Library ID
OL2459487M
Language
english
Format
DJVU
Filesize
498 kB (510076 bytes)
Series
Lecture Notes in Mathematics
Pages
158\158
Library
mexmat
Time added
2009-07-20 03:45:11

Description

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.

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