Geodesic
PERIOD IDENTITIES OF CM FORMS ON QUATERNION ALGEBRAS
Forum of Mathematics, Sigma, Tome 8 (2020)

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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. 
@article{10_1017_fms_2020_21,
     author = {CHARLOTTE CHAN},
     title = {PERIOD {IDENTITIES} {OF} {CM} {FORMS} {ON} {QUATERNION} {ALGEBRAS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {8},
     year = {2020},
     doi = {10.1017/fms.2020.21},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.21/}
}
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CHARLOTTE CHAN. PERIOD IDENTITIES OF CM FORMS ON QUATERNION ALGEBRAS. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.21

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