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arXiv · 2511.21798

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

Paul Boisseau
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Abstract

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.

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Paul Boisseau. 2025-11-26. Residues of Rankin-Selberg Zeta integrals and the split non-tempered Gan-Gross-Prasad conjectures. https://arxiv.org/abs/2511.21798

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