English

The distribution of $d_4(n)$ in arithmetic progressions

Number Theory 2024-04-09 v1

Abstract

We use the Petrow-Young [10] subconvexity bound for Dirichlet LL-functions to show that d4(n)d_4(n) has exponent of distribution 4/74/7 when we allow an average over aa mod qq, thereby giving an equidistribution result for d4(n)d_4(n) which goes past the 1/21/2 barrier for the first time.

Keywords

Cite

@article{arxiv.2404.04749,
  title  = {The distribution of $d_4(n)$ in arithmetic progressions},
  author = {Tomos Parry},
  journal= {arXiv preprint arXiv:2404.04749},
  year   = {2024}
}
R2 v1 2026-06-28T15:46:08.221Z