Related papers: On the global Gan-Gross-Prasad conjecture for gene…

We prove a conjectural formula relating the Bessel period of certain automorphic forms on $\mathrm{GSp}_4$ to a central $L$-value. This formula is proposed by Liu \cite{liu} as the refined Gan-Gross-Prasad conjecture for the groups…

We prove a precise formula relating the Bessel period of certain automorphic forms on ${\rm GSp}_{4}(\mathbb{A}_{F})$ to a central $L$-value. This is a special case of the refined Gan--Gross--Prasad conjecture for the groups $({\rm…

We state and prove an extension of the global Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary groups $U_n\times U_{n+1}$. Our theorems are based on a comparison of the…

In this paper, we prove the Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture for unitary groups $U_n\times U_{n+1}$ in all the endoscopic cases. Our main technical innovation is the computation of the contributions of certain…

In this paper, we establish a relationship between special periods and special L-values of automorphic representations of classical groups, and prove the non-tempered global Gan--Gross--Prasad conjecture in several cases. Our approach…

Using a relative trace formula approach, we prove the twisted global Gan-Gross-Prasad conjecture for $\operatorname{U}(V) \subseteq \operatorname{GL}(V)$, as well as its refinement, under some unramifiedness assumptions and local conditions…

The local non-tempered Gan-Gross-Prasad conjecture suggests that, for a pair of irreducible Arthur type representations of two successive general linear groups, they have a non-zero Rankin-Selberg period if and only if they are "relevant".…

We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,\pi\times\tau_1) L^S(s,\pi\times\tau_2)\cdots L^S(s,\pi\times\tau_r) \end{equation*} where $\pi$ is an…

In this paper we prove Conjecture \ref{conj1} for a set of representations of the group $GL_n({\bf A})$. This Conjecture is stated in complete generality as Conjecture 1 in \cite{G2}, and here we prove it for various cases. See Conjecture…

We prove a refinement of the global Gan-Gross-Prasad conjecture proposed by Ichino-Ikeda and N. Harris for unitary groups under some local conditions. We need to assume some expected properties of L-packets and some part of the local…

This is the third and the last of a series of three papers where we prove the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups and an Ichino--Ikeda type refinement. Our strategy is based on the comparison of…

In this paper, we prove one direction of the Gan--Gross--Prasad conjecture on metaplectic-symplectic groups for tempered cases. Furthermore, we also prove one direction of the non-tempered GGP conjecture for residual representations with…

In this paper we examine the saturation conjecture on decompositions of tensor products of irreducible representations for complex semisimple algebraic groups of type $D$ (the even \emph{spin} groups: Spin$(2n)$ for $n\ge 4$ an integer),…

In this paper, we introduce regularized trilinear periods on certain non-reductive groups. It has two direct applications. Firstly, it enables us to define the regularized Bessel periods and the regularized Fourier-Jacobi periods for all…

The local Gan-Gross-Prasad conjecture of unitary groups, which is now settled by the works of Plessis, Gan and Ichino, says that for a pair of generic $L$-parameters of $(U(n+1),U(n))$, there is a unique pair of representations in their…

We survey recent joint work with M. Rapoport and W. Zhang related to the arithmetic Gan-Gross-Prasad conjecture for Shimura varieties attached to unitary groups.

The endoscopic classification via the stable trace formula comparison provides certain character relations between irreducible cuspidal automorphic representations of classical groups and their global Arthur parameters, which are certain…

In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary $N\in \N$ and for {\it number fields}. The main new observation is a modification of a theorem due to Glenn Stevens for the…

In the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture, we formulate a local conjecture (arithmetic transfer) in the case of an exotic smooth formal moduli space of p-divisible groups, associated to a unitary…

We define variants of PEL type of the Shimura varieties that appear in the context of the Arithmetic Gan-Gross-Prasad conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global and semi-global) integral…