Gaussian test functions and Jacquet-Rallis transfer
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916905066954752 |
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| author | Mihatsch, Andreas Sankaran, Siddarth Yang, Tonghai |
| author_facet | Mihatsch, Andreas Sankaran, Siddarth Yang, Tonghai |
| contents | We construct Gaussian test functions for the general linear side of the Jacquet-Rallis relative trace formula comparison. These are functions which are defined in terms of their orbital integrals and transfer to the compact unitary group. Our construction relies on the formalism of Kudla-Millson and simple geometric properties of symmetric spaces. In particular, it also provides an explicit formula in terms of the Howe operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gaussian test functions and Jacquet-Rallis transfer Mihatsch, Andreas Sankaran, Siddarth Yang, Tonghai Representation Theory Number Theory 22E50, 11F27, 11F70 We construct Gaussian test functions for the general linear side of the Jacquet-Rallis relative trace formula comparison. These are functions which are defined in terms of their orbital integrals and transfer to the compact unitary group. Our construction relies on the formalism of Kudla-Millson and simple geometric properties of symmetric spaces. In particular, it also provides an explicit formula in terms of the Howe operator. |
| title | Gaussian test functions and Jacquet-Rallis transfer |
| topic | Representation Theory Number Theory 22E50, 11F27, 11F70 |
| url | https://arxiv.org/abs/2508.12598 |