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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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Table of 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.