Workshop: Mean Values of Long Dirichlet Polynomials with Divisor Coefficients, Alia Hamieh

Speaker
Alia Hamieh , University of Northern British Columbia

Abstract
The 2k-th moments and shifted moments of the Riemann zeta function can be modelled by mean values of Dirichlet polynomials with higher divisor coefficients. In this talk, I discuss recent work where we establish an asymptotic formula for mean values of long Dirichlet polynomials with higher order shifted divisor functions as coefficients, assuming a conjectural formula for a certain family of additive divisor sums. This proves a conjecture of Coney-Keating (2015) under the assumption of an additive divisor conjecture. We then use this result to establish a special case of a conjecture of Conrey-Gonek (1998) where the additive divisor conjecture is known. This talk is based on joint work with Fatma Cicek and Nathan Ng.