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A hybrid Euler-Hadamard product for the Riemann zeta function

Gonek, S.M., Hughes, C.P. and Keating, J.P. (2007) A hybrid Euler-Hadamard product for the Riemann zeta function. Duke Mathematical Journal, 136 (3). pp. 507-549. ISSN 0012-7094

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We use a smoothed version of the explicit formula to find an accurate pointwise approximation to the Riemann zeta function as a product over its nontrivial zeros multiplied by a product over the primes. We model the first product by characteristic polynomials of random matrices. This provides a statistical model of the zeta function which involves the primes in a natural way. We then employ the model in a heuristic calculation of the moments of the modulus of the zeta function on the critical line. For the second and fourth moments, we establish all of the steps in our approach rigorously. This calculation illuminates recent conjectures for these moments based on connections with random matrix theory

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 19 Jun 2009 09:52
Last Modified: 19 Jun 2009 09:52
Published Version: http://dx.doi.org/10.1215/S0012-7094-07-13634-2
Status: Published
Publisher: Duke University Press
Identification Number: 10.1215/S0012-7094-07-13634-2
URI: http://eprints.whiterose.ac.uk/id/eprint/5977

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