On simple zeros of the Riemann zeta-function

Abstract

We show that at least 19/27 of the zeros of the Riemann zeta-function are simple, assuming the Riemann Hypothesis (RH). This was previously established by Conrey, Ghosh and Gonek [Proc. London Math. Soc. 76 (1998), 497--522] under the additional assumption of the Generalised Lindelöf Hypothesis (GLH). We are able to remove this hypothesis by careful use of the generalised Vaughan identity.

Cited by in corpus (5)

• Hamiltonian for the zeros of the Riemann zeta function
• Lower bounds for discrete negative moments of the Riemann zeta function
• An upper bound for discrete moments of the derivative of the Riemann zeta-function
• Simple zeros of modular L-functions
• Multiplicity of nontrivial zeros of primitive L-functions via higher-level correlations