2 citations · 3 across the 9 of their papers we have counts for
9 papers
Co-periods and central symmetric cube L-values
Li Cai, Yangyu Fan, Dongming She
In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In t…
Euler systems and relative Satake isomorphism
Li Cai, Yangyu Fan, Shilin Lai
We explain how the unramified Plancherel formula in the relative Langlands program gives a natural way of constructing test vectors which satisfy the tame norm relations of an Eule…
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…
Higher Ext-groups and Relatively Supercuspidal Spectra
Li Cai, Yangyu Fan
Relatively supercuspidal representations are analogue of supercuspidal representations in the relative Langlands program. This work studies relatively supercuspidal representations…
Families of Canonical Local Periods on Spherical Varieties
Li Cai, Yangyu Fan
We consider the variation of canonical local periods on spherical varieties proposed by Sakellaridis-Venkatesh in families. We formulate conjectures for the rationality and meromor…