5 papers
Central values of Asai L-functions and twisted Gan--Gross--Prasad conjecture
Weixiao Lu, Danielle Wang, Zhiyu Zhang
We study certain new relative trace formulas on (non-reductive) period integrals involving Weil representations, in the context of the relative Langlands program. We study normal r…
Unitary Shimura varieties at ramified primes and arithmetic transfer
Yu Luo, Andreas Mihatsch, Zhiyu Zhang
We consider unitary Shimura varieties at places where the totally real field ramifies over $\mbQ$. Our first result constructs comparison isomorphisms between absolute and relative…
Non-reductive cycles and twisted arithmetic transfers for Shimura curves
Zhiyu Zhang
In this largely expository note, we explain some recent progress on new cycles on Shimura varieties and Rapoport-Zink spaces, (twisted) arithmetic fundamental lemma, and arithmetic…
Relative Fundamental Lemmas for Spherical Hecke Algebras and Multiplicative Hitchin Fibrations: the Jacquet--Rallis Case
X. Griffin Wang, Zhiyu Zhang
We prove the Jacquet--Rallis fundamental lemma for spherical Hecke algebras over local function fields using multiplicative Hitchin fibrations. Our work is inspired by the proof of…
Non-reductive special cycles and Twisted Arithmetic Fundamental Lemma
Zhiyu Zhang
We consider arithmetic analogs of the relative Langlands program and applications of new non-reductive geometry. Firstly, we introduce mirabolic special cycles, which produce speci…