Residues of Rankin-Selberg Zeta integrals and the split non-tempered Gan-Gross-Prasad conjectures

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Main Author: Boisseau, Paul
Format: Preprint
Published: 2025
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author Boisseau, Paul
author_facet Boisseau, Paul
contents We construct a regularization of the Rankin-Selberg period on general linear groups for non-tempered automorphic representations using residues of Zeta integrals. We prove that it satisfies the global non-tempered Gan-Gross-Prasad conjecture and its Ichino-Ikeda refinement. We also build a local version of our regularization and show that it defines a non-zero invariant linear form on non-tempered representations. Combined with previous works of Chan, Chen and Chen, this settles the conjectures over local fields of characteristic zero.
format Preprint
id arxiv_https___arxiv_org_abs_2511_21798
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Residues of Rankin-Selberg Zeta integrals and the split non-tempered Gan-Gross-Prasad conjectures
Boisseau, Paul
Number Theory
Representation Theory
We construct a regularization of the Rankin-Selberg period on general linear groups for non-tempered automorphic representations using residues of Zeta integrals. We prove that it satisfies the global non-tempered Gan-Gross-Prasad conjecture and its Ichino-Ikeda refinement. We also build a local version of our regularization and show that it defines a non-zero invariant linear form on non-tempered representations. Combined with previous works of Chan, Chen and Chen, this settles the conjectures over local fields of characteristic zero.
title Residues of Rankin-Selberg Zeta integrals and the split non-tempered Gan-Gross-Prasad conjectures
topic Number Theory
Representation Theory
url https://arxiv.org/abs/2511.21798