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Ichino period for CM forms
Li Cai, Yangyu Fan, Yong Jiang
In both local and global settings, we establish explicit relations between Ichino triple product period and Waldspurger toric periods for CM forms via the theta lifting and the see…
Spherical Characters in Families: the unitary Gan-Gross-Prasad case
Li Cai, Yangyu Fan
We consider the variation of spherical characters in families. We formulate conjectures for the rationality and meromorphic property of spherical characters. As an example, we esta…
Multiplicities of Representations in Algebraic Families
Li Cai, Yangyu Fan
In this short notes, we consider multiplicities of representations in general algebraic families, especially the upper semi-continuity of homological multiplicities and the locally…
-adic Waldspurger Formula for Non-split Primes and Converse of Gross--Zagier and Kolyvagin Theorem
Yangyu Fan, Xin Wan
Let be a prime and be an imaginary quadratic field. In this paper we generalize a recent construction of a new type of -adic -function and -adic Waldspur…
Higher Ext-groups in the triple product case
Li Cai, Yangyu Fan
In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product c…