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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.05021 |
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| _version_ | 1866915603459080192 |
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| author | Guitart, Xavier Molina, Santiago |
| author_facet | Guitart, Xavier Molina, Santiago |
| contents | We establish several formulas relating periods of modular forms on quaternion algebras over number fields to special values of L-functions. Our main inputs are the cohomological techniques for working with periods introduced in [Mol21], along with explicit versions of the Waldspurger formula due to Cai-Shu-Tian. We work in general even positive weights; when specialized to parallel weight 2, our formulas provide partial evidence for the conjectures of Oda and of Prasanna-Venkatesh in the case of forms associated to elliptic curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periods of modular forms and applications to the conjectures of Oda and of Prasanna-Venkatesh Guitart, Xavier Molina, Santiago Number Theory 11F67 (primary), 11G40 (secondary) We establish several formulas relating periods of modular forms on quaternion algebras over number fields to special values of L-functions. Our main inputs are the cohomological techniques for working with periods introduced in [Mol21], along with explicit versions of the Waldspurger formula due to Cai-Shu-Tian. We work in general even positive weights; when specialized to parallel weight 2, our formulas provide partial evidence for the conjectures of Oda and of Prasanna-Venkatesh in the case of forms associated to elliptic curves. |
| title | Periods of modular forms and applications to the conjectures of Oda and of Prasanna-Venkatesh |
| topic | Number Theory 11F67 (primary), 11G40 (secondary) |
| url | https://arxiv.org/abs/2507.05021 |