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We show that at least19    27of 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.

On simple zeros of the Riemann zeta‐function