Zegowitz, Stefanie
(2010)
*On the positive region of \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 often. 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 double project includes a complete proof of Lehman's theorem, in which two crucial constants are reduced. A further improvement on the Saouter-Demichel article leads to some new theorems.

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: | 06 Dec 2010 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/1547 |

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