Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

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

   

 

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
Published electronically: December 13, 2013
MathSciNet review: 3148519
Full-text PDF

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11M26, 11M06

Retrieve articles in all journals with MSC (2010): 11M26, 11M06


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: http://dx.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.