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Bibliographic Details
Main Authors: Suzuki, Miyu, Wakatsuki, Satoshi
Format: Preprint
Published: 2021
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.