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

Abstract

Assuming the Riemann hypothesis, we establish an upper bound for the $2k$-th discrete moment of the derivative of the Riemann zeta-function at nontrivial zeros, where $k$ is a positive real number. Our upper bound agrees with conjectures of Gonek and Hejhal and of Hughes, Keating, and O'Connell. This sharpens a result of Milinovich. Our proof builds upon a method of Adam Harper concerning continuous moments of the zeta-function on the critical line.

arXiv commentTo appear in Mathematika

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Cited by in corpus (7)

• Lower bounds for discrete negative moments of the Riemann zeta function
• Shifted moments of the Riemann zeta function
• Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli
• Moments of quadratic Dirichlet $L$-functions over Function Fields
• Lower bounds for negative moments of ${\zeta }^{\prime }(\rho )$
• Bounds for moments of cubic and quartic Dirichlet $L$-functions
• Moments of Dirichlet $L$-functions to a fixed modulus over function fields