On simple zeros of the Riemann zeta-function
Number Theory
2014-02-26 v1
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 Lindel\"of Hypothesis (GLH). We are able to remove this hypothesis by careful use of the generalised Vaughan identity.
Keywords
Cite
@article{arxiv.1302.5018,
title = {On simple zeros of the Riemann zeta-function},
author = {H. M. Bui and D. R. Heath-Brown},
journal= {arXiv preprint arXiv:1302.5018},
year = {2014}
}