Leírás
Abstract: In this talk we explore a distribution result for holomorphic Hecke cusp forms on the vertical geodesic. More precisely, we show how to evaluate the quantum variance of holomorphic Hecke cusp forms on the vertical geodesic for smooth, compactly supported test functions. The variance is related to an averaged shifted-convolution problem that we evaluate asymptotically. We encounter an off-diagonal term that matches exactly with a certain diagonal term, a feature reminiscent of moments of $L$-functions. During the talk we also compare the quantum variance computation for the vertical geodesic with the corresponding computation for the full fundamental domain and we highlight important differences.
The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.