English

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 LL-function of cube-free conductor. We also show a bound of the same strength for certain LL-functions of self-dual GL2\mathrm{GL}_2 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