**Title: **Algebraic twists of automorphic forms

**Speaker: **Yongxiao LIN，EPF Lausanne

**Abstract: **Given a fixed \rm GL_m-automorphic form F, it is tempting to show that the Fourier--Whittaker coefficients \lambda_F (n) of F do not correlate with the trace function K(n) of a general \ell-adic sheaf modulo q, in the convexity range q^{m/2}. We will discuss our new works in this direction for the \rm GL_3 and \rm GL_3\times \rm GL_2 cases, describe the connection of such a statement with some aspects of the subconvexity problem for L-functions, and mention some surrounding questions and challenges. This is based on joint works with E. Kowalski, Ph. Michel, and W. Sawin.

**Time/Venue: **2020年5月2日 02:00 下午

报告形式: 加入Room会议 https://us04web.zoom.us/j/78321144511