A note on the distribution of gaps between zeros of the Riemann zeta-function
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- by XiaoSheng Wu PDF
- Proc. Amer. Math. Soc. 142 (2014), 851-857 Request permission
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.References
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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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3148519