Leírás
Abstract: In this talk, I will talk about the cubic moment of cerntral $L$-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 $O(T^{8/7+\varepsilon})$ and Lindelöf-on-average bound on the short window $[T-M,T+M]$ for $M$ as small as $T^{\varepsilon}$. Ivić's results are improved in my recent work; in particular, Ivić's conjectured error term $O (T^{1+\varepsilon})$ 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.
The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.