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. This was previously established by Conrey, Ghosh and Gonek [Proc. London Math. Soc. 76 (1998) 497–522] under the additional assumption of the generalized Lindelöf hypothesis. We are able to remove this hypothesis by careful use of the generalized Vaughan identity.