Lethbridge Number Theory and Combinatorics Seminar: Nathan Ng

In this talk I will consider the discrete moments J_k(T) that are defined by summing the 2k-th power of the absolute value of the derivative of the Riemann zeta function zeta(s) at all nontrivial zeros of zeta(s) whose imaginary part has absolute value less than T. In the 1980's Steve Gonek and Dennis Hejhal (independently) studied these moments and proposed a conjecture for the size of J_k(T). I will give a survey of the known results towards the Gonek-Hejhal conjecture on J_k(T). If time permits, I will present several new results.