ULethbridge Number Theory and Combinatorics Seminar: Nathan Ng

The 2k-th moments I_k(T) of the Riemann zeta function have been studied extensively. In the late 90's, Keating-Snaith gave a conjecture for the size of I_k(T). At the same time Conrey-Gonek connected I_k(T) to mean values of long Dirichlet polynomials with divisor coefficients. Recently this has been further developed by Conrey-Keating in a series of 5 articles. I will discuss my work relating I_3(T) to smooth shifted ternary additive divisor sums and also recent joint work with Alia Hamieh on mean values of long Dirichlet polynomials with higher divisor coefficients.