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2006.94: A new bound for the smallest x with \pi(x) > \li(x)

2006.94: Kuok Fai Chao and Roger Plymen (2006) A new bound for the smallest x with \pi(x) > \li(x). math.NT/0509312. pp. 1-16.

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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
Uncontrolled Keywords:Number of primes up to x. Logarithmic integral. Riemann zeros. A bound for the first crossover.
Subjects:MSC 2000 > 11 Number theory
MIMS number:2006.94
Deposited By:Professor Roger Plymen
Deposited On:17 May 2006

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