Moments of the derivative of characteristic polynomials wirh an application to the Riemann zeta function

JB Conrey, MO Rubinstein, NC Snaith

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

We 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.
Translated title of the contributionMoments of the derivative of characteristic polynomials wirh an application to the Riemann zeta function
Original languageEnglish
Pages (from-to)611 - 629
JournalCommunications in Mathematical Physics
Volume267 (3)
Publication statusPublished - Nov 2006

Bibliographical note

Publisher: Springer
Other identifier: IDS number 082OJ

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