Residues of Rankin-Selberg Zeta integrals and the split non-tempered Gan-Gross-Prasad conjectures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912732037513216 |
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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 |