The Weyl bound for Dirichlet $L$-functions of cube-free conductor

Abstract

We prove a Weyl-exponent subconvex bound for any Dirichlet $L$-function of cube-free conductor. We also show a bound of the same strength for certain $L$-functions of self-dual $\mathrm{GL}_2$ automorphic forms that arise as twists of forms of smaller conductor.

Authors

Ian Petrow

ETH Zürich, Department of Mathematics, Rämistrasse 101, 8092 Zürich, Switzerland

Matthew P. Young

Department of Mathematics, Texas A&M University, College Station, TX 77843-3368