Unitary Friedberg-Jacquet periods and their twists: Relative trace formulas
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917968939581440 |
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| author | Leslie, Spencer Xiao, Jingwei Zhang, Wei |
| author_facet | Leslie, Spencer Xiao, Jingwei Zhang, Wei |
| contents | In a companion paper, we formulated 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 $\mathrm{GL}(2)$. In this paper, we introduce a new relative trace formula to prove our global conjecture under some local hypotheses. A new feature is the presence of relative endoscopy in the comparison. We also establish several local results on relative characters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unitary Friedberg-Jacquet periods and their twists: Relative trace formulas Leslie, Spencer Xiao, Jingwei Zhang, Wei Number Theory In a companion paper, we formulated 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 $\mathrm{GL}(2)$. In this paper, we introduce a new relative trace formula to prove our global conjecture under some local hypotheses. A new feature is the presence of relative endoscopy in the comparison. We also establish several local results on relative characters. |
| title | Unitary Friedberg-Jacquet periods and their twists: Relative trace formulas |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.09664 |