Explicit Constructions of Automorphic L-Functions

1. Front Matter

   Pages I-VI

   PDF

2. L-functions for the classical groups

   • I. Piatetski-Shapiro, S. Rallis

   Pages 1-52

3. L-functions for G×GL(n)

   • S. Gelbart, I. Piatetski-Shapiro

   Pages 53-136

4. Back Matter

   Pages 137-152

   PDF

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.

• algebra
• algebraic group
• number theory
• representation theory

Policies and ethics