Mean values of long Dirichlet polynomials with higher divisor coefficients

TL;DR

This paper derives an asymptotic formula for the mean values of long Dirichlet polynomials with higher divisor coefficients, assuming a conjecture, and verifies special cases of conjectures by Conrey-Keating.

Contribution

It introduces an asymptotic formula for these mean values under a conjecture and confirms specific cases of Conrey-Keating conjectures.

Findings

Proved an asymptotic formula for mean values of Dirichlet polynomials with higher divisor coefficients.

Validated special cases of Conrey-Keating conjectures.

Assumed a smoothed additive divisor conjecture for higher order functions.

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.