The Weyl bound for Dirichlet $L$-functions of cube-free conductor
Number Theory
2022-05-17 v3
Abstract
We prove a Weyl-exponent subconvex bound for any Dirichlet -function of cube-free conductor. We also show a bound of the same strength for certain -functions of self-dual automorphic forms that arise as twists of forms of smaller conductor.
Keywords
Cite
@article{arxiv.1811.02452,
title = {The Weyl bound for Dirichlet $L$-functions of cube-free conductor},
author = {Ian Petrow and Matthew P. Young},
journal= {arXiv preprint arXiv:1811.02452},
year = {2022}
}
Comments
Final version, to appear in Annals of Mathematics. We fixed a gap in the proof of the character sum estimate in section 9 using Deligne's semicontinuity theorem