On the Global Gan–gross–prasad Conjecture for Unitary Groups: Approximating Smooth Transfer of Jacquet–rallis

Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups

By the relative trace formula approach of Jacquet–Rallis, we prove the global Gan– Gross–Prasad conjecture for unitary groups under some local restrictions for the automorphic representations.

Fourier–jacobi Periods and the Central Value of Rankin–selberg L-functions

1.1. The refined Gan–Gross–Prasad conjecture. In this paper, as a sequel of [Xue14], we formulate a refinement to the global Gan–Gross–Prasad conjecture for the Fourier–Jacobi periods on U(n) × U(n) and prove it under some local conditions, assuming some expected properties of the L-packets and some parts of the local Gan–Gross–Prasad conjecture. This refinement is modeled on some recent work o...

On the smooth transfer conjecture of Jacquet–Rallis for n = 3

Refined Global Gan–gross–prasad Conjecture for Fourier–jacobi Periods on Symplectic Groups

In this paper, we propose a conjectural identity between the Fourier–Jacobi periods on symplectic groups and the central value of certain Rankin–Selberg L-functions. This identity can be viewed as a refinement to the global Gan–Gross–Prasad conjecture for Sp(2n)×Mp(2m). To support this conjectural identity, we show that when n = m and n = m±1, it can be deduced from the Ichino–Ikeda’s conjectur...

Arithmetic Theta Lifts and the Arithmetic Gan–gross–prasad Conjecture for Unitary Groups

In 1980s, Gross–Zagier [GZ86] established a formula that relates the Neron–Tate height of Heegner points on modular curves to the central derivative of certain L-functions associated to modular forms. Around the same time, Waldspurger proved a formula, relating toric periods of modular forms to the central value of certain L-functions. Gross put both of these formula in the framework of represe...