2025/11/26 by Paul Boisseau, Boisseau, Paul
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2511.21798
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.