Mean values of long Dirichlet polynomials with divisor coefficients

Fatma Cicek, Alia Hamieh, Nathan Ng

Published 2023-09-14Version 1

In this article, we prove an asymptotic formula for the mean value of long smoothed Dirichlet polynomials with divisor coefficients. Our result has a main term that includes all lower order terms and a power saving error term. This is derived from a more general theorem on mean values of long smoothed Dirichlet polynomials that was previously established by the second and third authors. We thus establish a stronger form of a conjecture of Conrey and Gonek in the case of divisor functions.