PERIOD IDENTITIES OF CM FORMS ON QUATERNION ALGEBRAS

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 th...

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Bibliographic Details
Published inForum of mathematics. Sigma Vol. 8
Main Author CHAN, CHARLOTTE
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 2020
Subjects
11F27
11F67
11R52
Identities
Norms
Quaternions
Toruses
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ISSN2050-5094
2050-5094
DOI10.1017/fms.2020.21

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Summary: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.
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ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2020.21