Abstract
Waldspurger’s formula gives an identity between the norm of a torus period and an
$L$
-function of the twist of an automorphic representation on GL(2). For any two Hecke characters of a fixed quadratic extension, one can consider the two torus periods coming from integrating one character against the automorphic induction of the other. Because the corresponding
$L$
-functions agree, (the norms of) these periods—which occur on different quaternion algebras—are closely related. In this paper, we give a direct proof of an explicit identity between the torus periods themselves.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Reference31 articles.
1. [Y95] Yang, T. , ‘Theta liftings and the $L$ -function of elliptic curves’, PhD Thesis, University of Maryland, College Park, 1995, 126 pages, ProQuest LLC.
2. Central values of L-functions over CM fields
3. Sur les valeurs de certaines fonctions L automorphes en leur centre de symétrie;Waldspurger;Compos. Math.,1985
4. Representation of Lie Groups and Special Functions
5. Local ε-Factors and Characters of GL(2)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Ichino periods for CM forms;Journal of Number Theory;2025-01
2. On Triple Product L-Functions and a Conjecture of Harris–Venkatesh;International Mathematics Research Notices;2023-07-24