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

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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 times the average spacing and that a positive proportion of the time, the gap between consecutive zeros is larger than 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:
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.