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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2103.04589 |
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| _version_ | 1866914821039980544 |
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| author | Suzuki, Miyu Wakatsuki, Satoshi |
| author_facet | Suzuki, Miyu Wakatsuki, Satoshi |
| contents | Let $F$ be a number field and $D$ a quaternion algebra over $F$. Take a cuspidal automorphic representation $π$ of $D_{\mathbb{A}}^\times$ with trivial central character and a cusp form $ϕ$ in $π$. Using the prehomogeneous zeta function, we find an explicit mean value of the toric periods of $ϕ$ with respect to quadratic algebras over $F$. The result can also be written as a mean value formula for the central values of automorphic $L$-functions twisted by quadratic characters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_04589 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Explicit mean value theorems for toric periods and automorphic $L$-functions Suzuki, Miyu Wakatsuki, Satoshi Number Theory Let $F$ be a number field and $D$ a quaternion algebra over $F$. Take a cuspidal automorphic representation $π$ of $D_{\mathbb{A}}^\times$ with trivial central character and a cusp form $ϕ$ in $π$. Using the prehomogeneous zeta function, we find an explicit mean value of the toric periods of $ϕ$ with respect to quadratic algebras over $F$. The result can also be written as a mean value formula for the central values of automorphic $L$-functions twisted by quadratic characters. |
| title | Explicit mean value theorems for toric periods and automorphic $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2103.04589 |