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arXiv · 1807.09435

Period identities of CM forms on quaternion algebras

Charlotte Chan
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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.

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Charlotte Chan. 2018-07-25. Period identities of CM forms on quaternion algebras. https://doi.org/10.1017/fms.2020.21

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