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) |
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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: | https://eprints.maths.manchester.ac.uk/id/eprint/1541 |

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