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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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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