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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the gaps between consecutive zeros of the Riemann zeta-function


Authors: H. M. Bui, M. B. Milinovich and N. C. Ng
Journal: Proc. Amer. Math. Soc. 138 (2010), 4167-4175
MSC (2010): Primary 11M26; Secondary 11M06
Published electronically: May 28, 2010
MathSciNet review: 2680043
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Abstract: Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and that infinitely often they differ by at least 2.6950 times the average spacing.


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Additional Information

H. M. Bui
Affiliation: Mathematical Institute, University of Oxford, Oxford, OX1 3LB United Kingdom
Email: hung.bui@maths.ox.ac.uk

M. B. Milinovich
Affiliation: Department of Mathematics, University of Mississippi, University, Mississippi 38677
Email: mbmilino@olemiss.edu

N. C. Ng
Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, Canada T1K 3M4
Email: ng@cs.uleth.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10443-4
PII: S 0002-9939(2010)10443-4
Keywords: Distribution of zeros, Riemann Hypothesis, Riemann zeta-function
Received by editor(s): September 5, 2009
Received by editor(s) in revised form: February 9, 2010
Published electronically: May 28, 2010
Additional Notes: The first author was supported by an EPSRC Postdoctoral Fellowship
The second author was supported in part by a University of Mississippi College of Liberal Arts summer research grant
The third author was supported in part by an NSERC Discovery grant
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.