  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.
