Lower bounds for discrete negative moments of the Riemann zeta function

Abstract

We prove lower bounds for the discrete negative $2k$th moment of the\nderivative of the Riemann zeta function for all fractional $k\\geqslant 0$. The\nbounds are in line with a conjecture of Gonek and Hejhal. Along the way, we\nprove a general formula for the discrete twisted second moment of the Riemann\nzeta function. This agrees with a conjecture of Conrey and Snaith.\n