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On the extreme values of the Riemann zetafunction between its zeros on the critical line

Hall, R.R. (2003) On the extreme values of the Riemann zetafunction between its zeros on the critical line. Journal für die reine und angewandte Mathematik (Crelle's Journal), 560. pp. 29-41. ISSN 1435-5345

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Abstract

We give new upper bounds (for every theta) of the form

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where {t(n)} is the sequence of distinct zeros of \zeta(1/2 + it)\ in R+ and M-n is the maximum between t(n) and t(n+1), k = 1,2. In particular we show that for small theta we have H-k(theta) << theta(3) (with explicit constants): this result might be viewed as unconditional, positive evidence for part of Montgomery's Pair Correlation Conjecture, relating to the small gaps between zeros.

Item Type: Article
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 10 Feb 2009 10:56
Last Modified: 10 Feb 2009 16:18
Published Version: http://dx.doi.org/10.1515/crll.2003.059
Status: Published
Publisher: Walter de Gruyter GmbH & Co. KG
Identification Number: 10.1515/crll.2003.059
URI: http://eprints.whiterose.ac.uk/id/eprint/7669

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