4 papers
-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…
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…
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…
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…