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.

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Authors

Ian Petrow

ETH Zürich, Zürich, Switzerland

Current address:

University College London, London, United Kingdom Matthew P. Young

Texas A&M University College Station, TX, USA