English

The $L^1$ mean of the exponential sum of the divisor function

Number Theory 2025-06-04 v2

Abstract

We give a relatively simple proof that 01nxd(n)e(nα)dαx. \int _0^1\left |\sum _{n\leq x}d(n)e(n\alpha )\right |d\alpha \asymp \sqrt x.

Keywords

Cite

@article{arxiv.2404.04747,
  title  = {The $L^1$ mean of the exponential sum of the divisor function},
  author = {Tomos Parry},
  journal= {arXiv preprint arXiv:2404.04747},
  year   = {2025}
}