Moments of the derivative of the Riemann zeta-function and of characteristic polynomials

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dc.creatorConrey, J. Brian
dc.creatorRubinstein, Michael O.
dc.creatorSnaith, Nina C.
dc.date2005-08-19
dc.date2006-03-17
dc.date.accessioned2026-07-07T06:42:48Z
dc.date.available2026-07-07T06:42:48Z
dc.descriptionWe investigate the moments of the derivative, on the unit circle, of characteristic polynomials of random unitary matrices and use this to formulate a conjecture for the moments of the derivative of the Riemann zeta-function on the critical line. We do the same for the analogue of Hardy's Z-function, the characteristic polynomial multiplied by a suitable factor to make it real on the unit circle. Our formulae are expressed in terms of a determinant of a matrix whose entries involve the I-Bessel function and, alternately, by a combinatorial sum.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/0508378
dc.identifierhttp://arxiv.org/abs/math/0508378
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102180
dc.subjectNumber Theory
dc.subjectMathematical Physics
dc.subject11M06, 15A52
dc.titleMoments of the derivative of the Riemann zeta-function and of characteristic polynomials
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