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arXiv · 1302.5018

On simple zeros of the Riemann zeta-function

H. M. Bui·D. R. Heath-Brown
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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.

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H. M. Bui, D. R. Heath-Brown. 2013-02-20. On simple zeros of the Riemann zeta-function. https://doi.org/10.1112/blms%2Fbdt026

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