Twisted period integrals and applications
Zhiyu Zhang (Stanford University)

The Waldspurger formula reveals a striking relation between twisted versions of Hecke periods and central L-values of modular forms. The use of quadratic twists is crucial in many applications, including equidistribution of integer points on spheres and of Heegner points. In this talk, I will present the twisted Gan-Gross-Prasad conjecture on twisted versions of tensor product L-functions. In particular, it provides new information on twisted symmetric square L-functions of modular forms, via the Langlands transfer of quadratic base change. I will outline a proof of this conjecture under some local assumptions, based on joint work with Lu and Wang. There are some essential differences compared to untwisted settings, leading to new applications and new questions.

Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).