Rankin-Selberg convolutions for GL(n)×GL(n) and GL(n)×GL(n−1) for principal series representations

Jian Shu Li, Dongwen Liu, Feng Su*, Binyong Sun

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let k be a local field. Let Iv and Iv′ be smooth principal series representations of GLn(k) and GLn-−1(k), respectively. The Rankin-Selberg integrals yield a continuous bilinear map Iv×Iv′→C with a certain invariance property. We study integrals over a certain open orbit that also yield a continuous bilinear map Iv×Iv′→C with the same invariance property, and show that these integrals equal the Rankin-Selberg integrals up to an explicit constant. Similar results are also obtained for Rankin-Selberg integrals for GLn(k) × GLn(k).

Original languageEnglish
Pages (from-to)2203-2218
Number of pages16
JournalScience China Mathematics
Volume66
Issue number10
DOIs
Publication statusPublished - Oct 2023

Keywords

  • 22E50
  • 43A80
  • L-functions
  • Rankin-Selberg convolutions
  • principal series representations

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