Explicit Constructions of Automorphic L-Functions

  • Authors
  • Stephen Gelbart
  • Ilya Piatetski-Shapiro
  • Stephen Rallis

Part of the Lecture Notes in Mathematics book series (LNM, volume 1254)

Table of contents

  1. Front Matter
    Pages I-VI
  2. I. Piatetski-Shapiro, S. Rallis
    Pages 1-52
  3. S. Gelbart, I. Piatetski-Shapiro
    Pages 53-136
  4. Back Matter
    Pages 137-152

About this book

Introduction

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.

Keywords

algebra algebraic group number theory representation theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0078125
  • Copyright Information Springer-Verlag Berlin Heidelberg 1987
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-17848-4
  • Online ISBN 978-3-540-47880-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book