On simple zeros of the Riemann zeta-function

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 Lindel"of Hypothesis (GLH). We are able to remove this hypothesis by careful use of the generalised Vaughan identity.