Related papers: Refined global Gross-Prasad conjecture on special …

We investigate the Gross-Prasad conjecture and its refinement for the Bessel periods in the case of $\left(\mathrm{SO}\left(5\right),\mathrm{SO}\left(2\right)\right)$. In particular, by combining several theta correspondences, we prove the…

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…

For automorphic representations in the nontempered cuspidal spectrum of $\mathrm{SO}_5$, we prove the refined Gan-Gross-Prasad conjecture by establishing a precise Bessel period formula, in which the square of the global Bessel period is…

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 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 \cite{Ha}, Neal Harris has given a refined Gross-Prasad conjecture for unitary group as an analogue of Ichino and Ikeda's paper \cite{Ich} concerning special orthogonal groups. In his paper, he stated a conjecture under the assumption…

We formulate an explicit refinement of B\"ocherer's conjecture for Siegel modular forms of degree 2 and squarefree level, relating weighted averages of Fourier coefficients with special values of L-functions. To achieve this, we compute the…

In this paper we will study certain models of irreducible admissible representations of the split special orthogonal group $SO(2n+1)$ over a nonarchimedean local field. If $n=1$, these models were considered by Waldspurger. If $n=2$, they…

Given irreducible representations $\Pi$ and $\pi$ of the rank one special orthogonal groups $G=SO(n+1,1)$ and $G'=SO(n,1)$ with nonsingular integral infinitesimal character, we state in terms of $\theta$-stable parameter necessary and…

Let F be a non-archimedean local field, of characteristic 0. Let V be a finite dimensional vector space over F and q be a non-degenerate quadratic form on V. Denote d the dimension of V and G=SO(d) the special orthogonal group of (V,q). Let…

Let $F$ be a non-archimedean local field, of characteristic 0. Let $V$ be a finite dimensional vector space over $F$ and $q$ be a non-degenerate quadratic form on $V$. Denote $G$ the special orthogonal group of $(V,q)$. Let $W$ a…

Let $\pi$ be a cuspidal automorphic representation of PGL($2n$) over a number field $F$, and $\eta$ the quadratic idele class character attached to a quadratic extension $E/F$. Guo and Jacquet conjectured a relation between the nonvanishing…

This is the first 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 relative trace…

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 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…

Let F be a number field, A_F its ring of adeles, and let {\pi}_n and {\pi}_{n+1} be irreducible, cuspidal, automorphic representations of SO_n(A_F) and SO_{n+1}(A_F), respectively. In 1991, Benedict Gross and Dipendra Prasad conjectured the…

We demonstrate that for symmetric cubes of algebraic regular Hecke eigenforms on $\mathrm{GL}(2)$, a decorrelation phenomenon occurs for global Bessel periods of $\mathrm{SO}(5)\times \mathrm{SO}(2)$ averaged over imaginary quadratic…

We prove the local Gross-Prasad conjecture for tempered representations of special orthogonal groups. Roughly speaking, the conjecture says that, if sigma is an irreducible representation of SO(n) and rho is an irreducible representation of…

Lapid and Mao conjectured Ichino-Ikeda type formula of Whittaker periods for any quasi-split reductive groups and metaplectic groups. In this paper, we prove this formula for any irreducible cuspidal globally generic automorphic…

This is the second 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 relative trace…