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Large spaces between the zeros of the Riemann zeta-function and random matrix theory

Hall, R.R. (2004) Large spaces between the zeros of the Riemann zeta-function and random matrix theory. Journal of Number Theory, 109 (2). pp. 240-265. ISSN 0022-314X

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Abstract

On the hypothesis that the 2k-th mixed moments of Hardy's Z-function and its derivative are correctly predicted by random matrix theory, it is established that large gaps (depending on, and apparently increasing with k) exist between the zeta zeros. The case k=3 has been worked out in an earlier paper (in this journal) and the cases k=4,5,6 are considered here. When k=6 the gaps obtained have >4 times the average gap length. This depends on calculations involving Jacobi-Schur functions and formulae for these functions due to Jacobi, Trudi and Aitken in the classical theory of equations.

Item Type: Article
Keywords: Riemann zeta-function; Random matrix theory; Jacobi-Schur functions
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 01 Jun 2009 12:18
Last Modified: 01 Jun 2009 12:18
Published Version: http://dx.doi.org/10.1016/j.jnt.2004.01.007
Status: Published
Publisher: Elsevier Science B.V. Amsterdam
Identification Number: 10.1016/j.jnt.2004.01.007
URI: http://eprints.whiterose.ac.uk/id/eprint/6765

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