Pair correlation of the zeros of the derivative of the Riemann $ξ$-function

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dc.creatorFarmer, David W.
dc.creatorGonek, Steven M.
dc.date2008-03-04
dc.date.accessioned2026-07-07T09:24:33Z
dc.date.available2026-07-07T09:24:33Z
dc.descriptionThe complex zeros of the Riemannn zeta-function are identical to the zeros of the Riemann xi-function, $ξ(s)$. Thus, if the Riemann Hypothesis is true for the zeta-function, it is true for $ξ(s)$. Since $ξ(s)$ is entire, the zeros of $ξ'(s)$, its derivative, would then also satisfy a Riemann Hypothesis. We investigate the pair correlation function of the zeros of $ξ'(s)$ under the assumption that the Riemann Hypothesis is true. We then deduce consequences about the size of gaps between these zeros and the proportion of these zeros that are simple.
dc.description28 pages. 3 figures
dc.identifierhttps://arxiv.org/abs/0803.0425
dc.identifierhttp://arxiv.org/abs/0803.0425
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156138
dc.subjectNumber Theory
dc.subjectMathematical Physics
dc.subject11M26
dc.titlePair correlation of the zeros of the derivative of the Riemann $ξ$-function
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