Asymptotic for the Cubic Moment of Maass Form L-Functions

In this talk, I will talk about the cubic moment of central L-values for Maass forms. It was studied by Aleksandar Ivić at the beginning of this century, obtaining asymptotic on the long interval [0, T] with error term O(T8/7+ε) and Lindelöf-on-average bound on the short window [T-M, T+M] for M as small as Tε. Ivić’s results are improved in my recent work; in particular, Ivić’s conjectured error term O(T1+ε) is proven. Our proof follows the standard Kuznetsov–Voronoi approach stemed from the work of Conrey and Iwaniec. Our main new idea is a combination of the methods of Xiaoqing Li and Young.