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


Author: XiaoSheng Wu
Journal: Proc. Amer. Math. Soc. 142 (2014), 851-857
MSC (2010): Primary 11M26, 11M06
DOI: https://doi.org/10.1090/S0002-9939-2013-11833-2
Published electronically: December 13, 2013
MathSciNet review: 3148519
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Abstract | References | Similar Articles | Additional Information

Abstract: Assuming the Riemann Hypothesis, we prove that a positive proportion of the time, the gap between consecutive zeros of the Riemann zeta-function is smaller than $ 0.6553$ times the average spacing and that a positive proportion of the time, the gap between consecutive zeros is larger than $ 1.6989$ times the average spacing.


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Additional Information

XiaoSheng Wu
Affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Address at time of publication: School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China
Email: xswu@amss.ac.cn

DOI: https://doi.org/10.1090/S0002-9939-2013-11833-2
Keywords: Gaps, zeros, Riemann zeta-function
Received by editor(s): March 9, 2011
Received by editor(s) in revised form: March 22, 2012, and April 23, 2012
Published electronically: December 13, 2013
Additional Notes: The author is partially supported by the National Natural Science Foundation of China (grant No. 11271352) and the Chinese Universities Scientific Fund (grant No. WK0010000031)
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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