Rankin-Selberg periods for spherical principal series

Jan Frahm; Feng Su

doi:10.1007/s00229-021-01295-6

Rankin-Selberg periods for spherical principal series

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer 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.

Originalsprog	Engelsk
Tidsskrift	Manuscripta Mathematica
Vol/bind	168
Nummer	1-2
Sider (fra-til)	1-33
Antal sider	33
ISSN	0025-2611
DOI	https://doi.org/10.1007/s00229-021-01295-6
Status	Udgivet - maj 2022

Adgang til dokumentet

10.1007/s00229-021-01295-6

https://arxiv.org/pdf/1706.05167

Symmetry Breaking in Mathematics
Frahm, J. (PI), Weiske, C. (Deltager), Ditlevsen, J. (Deltager), Spilioti, P. (Deltager), Bang-Jensen, F. J. (Deltager) & Labriet, Q. (Deltager)
01/08/2019 → 31/07/2024
Projekter: Projekt › Forskning

Citationsformater

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AB - 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.

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KW - SUBCONVEXITY

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Rankin-Selberg periods for spherical principal series

Abstract

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Fingeraftryk

Projekter

Symmetry Breaking in Mathematics

Citationsformater