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The Rankin–Selberg method for automorphic distributions

  • Stephen D. Miller
  • , Wilfried Schmid

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This paper describes our method of pairing automorphic distributions.We present a third technique for obtaining the analytic properties of automorphic L-functions, in addition to the existing methods of integral representations (Rankin–Selberg) and Fourier coefficients of Eisenstein series (Langlands–Shahidi). We recently used this technique to establish new cases of the full analytic continuation of the exterior square L-functions. The paper here gives an exposition of our method in two special, yet representative cases: the Rankin–Selberg tensor product L-functions for PGL(2,Z)∖PGL(2,R), as well as for the exterior square L-functions for GL(4,Z)∖GL(4,R).

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages111-150
Number of pages40
DOIs
StatePublished - 2008

Publication series

NameProgress in Mathematics
Volume255
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Keywords

  • Analytic L-functions
  • Automorphic distributions
  • Exterior square
  • Integral representations
  • Rankin–Selberg

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