Mon, April 13, 2026
4:00 pm - 5:00 pm
Math Tower (MW) 154
Liyang Yang
Cal Tech
Title
Weyl Bounds for $\mathrm{GL}_2$ Beyond Positivity
Abstract
The subconvexity problem is a central theme in the analytic theory of $L$-functions and a major testing ground for modern analytic techniques. In this talk, I will present a Weyl-type subconvex bound in the level aspect for $\mathrm{GL}_2$ over number fields, in a setting beyond the reach of the cubic moment method. The result applies to cuspidal forms of level $p^3$, corresponding to the case of minimal wild ramification, with arbitrary nebentypus. The proof is based on a refined duality for the fourth moment and a conductor-lowering phenomenon on the dual side.