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 . Our method applies our recent conjecture together with Laporta, for the modified Selberg integral of , 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 $d_3$