Aarhus University Seal

Rankin-Selberg periods for spherical principal series

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Links

DOI

  • Jan Frahm
  • Feng Su, Xi'an Jiaotong-Liverpool University, China

By the unfolding method, Rankin–Selberg L-functions for GL(n)×GL(n′) can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor products of the relevant automorphic representations. By the multiplicity-one theorems due to Sun–Zhu and Chen–Sun such invariant forms are unique up to scalar multiples and can therefore be related to invariant forms on equivalent principal series representations. We construct meromorphic families of such invariant forms for spherical principal series representations of GL(n,R) and conjecture that their special values at the spherical vectors agree in absolute value with the archimedean local L-factors of the corresponding L-functions. We verify this conjecture in several cases. This work can be viewed as the first of two steps in a technique due to Bernstein–Reznikov for estimating L-functions using their period integral expressions.

Original languageEnglish
JournalManuscripta Mathematica
Volume168
Issue1-2
Pages (from-to)1-33
Number of pages33
ISSN0025-2611
DOIs
Publication statusPublished - 2022

    Research areas

  • BOUNDS, GL(N), SUBCONVEXITY

See relations at Aarhus University Citationformats

Projects

ID: 177054904