SFU Number Theory and Algebraic Seminar: Alia Hamieh (Online)

In this talk, I report on recent work with Nathan Ng. Assuming a conjectural formula for a certain family of additive divisor sums, we prove an asymptotic formula for mean values of long Dirichlet polynomials with higher order shifted divisor functions as coefficients. This establishes a conjecture of Coney-Keating under the assumption of an additive divisor conjecture. As a consequence, we prove a special case of a conjecture of Conrey-Gonek when the additive divisor conjecture is known.