Mean values of long Dirichlet polynomials with higher divisor coefficients

Alia Hamieh, Nathan Ng

Published 2021-05-07Version 1

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 \cite{CK3} on mean values of long Dirichlet polynomials with higher order shifted divisor functions as coefficients.