English

On the Selberg integral of the three-divisor function $d_3$

Number Theory 2012-10-02 v3

Abstract

We give a new non-trivial upper bound for the Selberg integral of the three-divisor function d3(n)d_3(n). Our method applies our recent conjecture together with Laporta, for the modified Selberg integral of d3(n)d_3(n), and a kind of modified Gallagher Lemma for the exponential sums.

Keywords

Cite

@article{arxiv.1207.0902,
  title  = {On the Selberg integral of the three-divisor function $d_3$},
  author = {Giovanni Coppola},
  journal= {arXiv preprint arXiv:1207.0902},
  year   = {2012}
}

Comments

Selberg integral of $d_3$ exponent is improved to 6/5, applying conjectural exponent 1 for the modified Selberg integral of $d_3$

R2 v1 2026-06-21T21:30:14.330Z