### Abstract

Two of the most important areas in analytic number theory concern counting the number of zeros of zeta functions on and off the line, and in beating subconvexity bounds. Both types of results can be obtained from knowing moments of the zeta function multiplied by a Dirichlet polynomial. In this talk we present an asymptotic formula for the fourth moment of the zeta function multiplied by a Dirichlet polynomial, and conjecture a formula for general moments.