English

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.

Keywords

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

R2 v1 2026-06-24T01:53:34.441Z