Number Theory Seminar

The subconvexity problem for GL(1)-twists of a fixed GL(3) cusp form (solved by R. Munshi in 2015) is equivalent to establishing that Dirichlet characters $\chi$ modulo $q$ do not correlate with the Fourier Whittaker coefficients of the given GL(3) form in the convexity range $q^{3/2}$. In this talk, we will explain how a recent alternative proof of Munshi's theorem -due to R. Holowinsky and P. Nelson- makes it possible to replace the character $\chi$ by the trace function of a general $\ell$-adic sheaf modulo $q$ (when $q$ is prime).

This is joint with E. Kowalski, Y. Lin and W. Sawin.