Mean values of long Dirichlet polynomials with higher divisor coefficients
Number Theory
2022-10-18 v2
Abstract
In this article, we prove an asymptotic formula for mean values of long Dirichlet polynomials with higher order shifted divisor functions, assuming a smoothed additive divisor conjecture for higher order shifted divisor functions. As a consequence of this work, we prove special cases of conjectures of Conrey-Keating on mean values of long Dirichlet polynomials with higher order shifted divisor functions as coefficients.
Cite
@article{arxiv.2105.03525,
title = {Mean values of long Dirichlet polynomials with higher divisor coefficients},
author = {Alia Hamieh and Nathan Ng},
journal= {arXiv preprint arXiv:2105.03525},
year = {2022}
}
Comments
Final version. 50 pages. Accepted by Advances in Mathematics