Rankin-Selberg periods for spherical principal series

Jan Frahm, Feng Su*

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Abstract

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.

OriginalsprogEngelsk
TidsskriftManuscripta Mathematica
Vol/bind168
Nummer1-2
Sider (fra-til)1-33
Antal sider33
ISSN0025-2611
DOI
StatusUdgivet - 2022

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  • Symmetry Breaking in Mathematics

    Frahm, J. (PI), Weiske, C. (Deltager), Ditlevsen, J. (Deltager), Spilioti, P. (Deltager), Bang-Jensen, F. J. (Deltager) & Labriet, Q. (Deltager)

    01/08/201931/07/2024

    Projekter: ProjektForskning

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