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 derivative of the Riemann zeta function for all fractional $k⩾0$. The bounds are in line with a conjecture of Gonek and Hejhal. Along the way, we prove a general formula for the discrete twisted second moment of the Riemann zeta function. This agrees with a conjecture of Conrey and Snaith.

42 pages

References in corpus (2)

• An upper bound for discrete moments of the derivative of the Riemann zeta-function
• High pseudomoments of the Riemann zeta function

Cited by in corpus (2)

• An annotated bibliography for comparative prime number theory
• Lower bounds for negative moments of ${\zeta }^{\prime }(\rho )$