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


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.


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