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

Tahir, Munibah (2010) A new bound for the smallest x with \pi(x) > li(x). Masters thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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Abstract

The difference \pi(x) - li(x) has been the subject of lively interest since Littlewood's theorem (1914) that \pi(x) - li(x) changes sign infinitely many times. The issue is to find an upper bound for the first crossover. Two papers on this issue were published in July 2010: Chao-Plymen, Int. J. Number Theory 6 (2010) 681-690, and Saouter-Demichel, Math. Comp. 79 (2010) 2395 - 2405. This dissertation is a very detailed analysis of these two articles. A new theorem (assuming the Riemann Hypothesis) is discovered: see Chapter 7. This theorem (assuming the Riemann Hypothesis) is the best known result.

Item Type: Thesis (Masters)
Uncontrolled Keywords: Primes, logarithmic integral, first crossover
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory
Depositing User: Professor Roger Plymen
Date Deposited: 15 Nov 2010
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1541

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