Chao, Kuok Fai and Plymen, Roger (2006) A new bound for the smallest x with \pi(x) > \li(x). math.NT/0509312. pp. 1-16. (Submitted)
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Official URL: http://arxiv.org/abs/math.NT/0509312
Abstract
We reduce the dominant term in Lehman's theorem. This improved estimate allows us to refine the main theorem of Bays & Hudson. Entering 2,000,000 Riemann zeros, we prove that there exists x in the interval [1.39792101 \times 10^316, 1.39847603 \times 10^316] for which \pi(x) > \li(x). This interval is strictly a sub-interval of the interval in Bays & Hudson [1], and is narrower by a factor of about 10.
Item Type: | Article |
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Uncontrolled Keywords: | Number of primes up to x. Logarithmic integral. Riemann zeros. A bound for the first crossover. |
Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory |
Depositing User: | Professor Roger Plymen |
Date Deposited: | 17 May 2006 |
Last Modified: | 20 Oct 2017 14:12 |
URI: | https://eprints.maths.manchester.ac.uk/id/eprint/106 |
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- A new bound for the smallest x with \pi(x) > \li(x). (deposited 17 May 2006) [Currently Displayed]
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