Liangxun Li: Variance estimate for Eisenstein series and moments of $L$-functions

Abstract: In this talk, I will present the proof of our variance estimate for the cubic moment of Eisenstein series. Our approach relies on the Lindel\"of-on-average type bounds for various $L$-functions, particularly Rankin--Selberg $L$-functions at the special points $1/2+it_j$. I will also discuss related developments for Rankin--Selberg $L$-functions of higher degree and explain the common ideas underlying these results. This is a continuation of our previous talk on the value distribution of automorphic forms.