Unitary Friedberg-Jacquet periods and their twists: Fundamental lemmas
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915194732544000 |
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| author | Leslie, Spencer Xiao, Jingwei Zhang, Wei |
| author_facet | Leslie, Spencer Xiao, Jingwei Zhang, Wei |
| contents | We formulate a global conjecture for the automorphic period integral associated to the symmetric pairs defined by unitary groups over number fields, generalizing a theorem of Waldspurger's toric period for $\mathrm{GL}(2)$. We introduce a new relative trace formula to prove our global conjecture under some local hypotheses. A new feature is the presence of the relative endoscopy. In this paper we prove the main local theorem: a new relative fundamental lemma comparing certain orbital integrals of functions matched in terms of Hironaka and Satake transforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unitary Friedberg-Jacquet periods and their twists: Fundamental lemmas Leslie, Spencer Xiao, Jingwei Zhang, Wei Number Theory We formulate a global conjecture for the automorphic period integral associated to the symmetric pairs defined by unitary groups over number fields, generalizing a theorem of Waldspurger's toric period for $\mathrm{GL}(2)$. We introduce a new relative trace formula to prove our global conjecture under some local hypotheses. A new feature is the presence of the relative endoscopy. In this paper we prove the main local theorem: a new relative fundamental lemma comparing certain orbital integrals of functions matched in terms of Hironaka and Satake transforms. |
| title | Unitary Friedberg-Jacquet periods and their twists: Fundamental lemmas |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.09500 |