A note on a conjecture of Gonek

Abstract

We derive a lower bound for a second moment of the reciprocal of the derivative of the Riemann zeta-function averaged over the zeros of the zeta-function that is half the size of the conjectured value. Our result is conditional upon the assumption of the Riemann Hypothesis and the conjecture that the zeros of the zeta-function are simple.

10 pages, to appear in Funct. Approx. Comment. Math

References in corpus (3)

• Lower bounds for moments of L-functions
• A note on the gaps between consecutive zeros of the Riemann zeta-function
• Upper bounds for the moments of zeta prime rho

Cited by in corpus (4)

• Lower bounds for discrete negative moments of the Riemann zeta function
• Simple zeros of modular L-functions
• An annotated bibliography for comparative prime number theory
• Lower bounds for negative moments of ${\zeta }^{\prime }(\rho )$