On triple product $L$-functions and the fiber bundle method
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913814524461056 |
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| author | Getz, Jayce R. Gu, Miao Pam Hsu, Chun-Hsien Leslie, Spencer |
| author_facet | Getz, Jayce R. Gu, Miao Pam Hsu, Chun-Hsien Leslie, Spencer |
| contents | We introduce multi-variable zeta integrals which unfold to Euler products representing the triple product $L$-function times a product of $L$-functions with known analytic properties. We then formulate a generalization of the Poisson summation conjecture and show how it implies the analytic properties of triple product $L$-functions. Finally, we propose a strategy, the fiber bundle method, to reduce this generalized conjecture to a simpler case of the Poisson summation conjecture along with certain local compatibility statements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On triple product $L$-functions and the fiber bundle method Getz, Jayce R. Gu, Miao Pam Hsu, Chun-Hsien Leslie, Spencer Number Theory Representation Theory 11F66, 11F70 We introduce multi-variable zeta integrals which unfold to Euler products representing the triple product $L$-function times a product of $L$-functions with known analytic properties. We then formulate a generalization of the Poisson summation conjecture and show how it implies the analytic properties of triple product $L$-functions. Finally, we propose a strategy, the fiber bundle method, to reduce this generalized conjecture to a simpler case of the Poisson summation conjecture along with certain local compatibility statements. |
| title | On triple product $L$-functions and the fiber bundle method |
| topic | Number Theory Representation Theory 11F66, 11F70 |
| url | https://arxiv.org/abs/2503.21648 |