## 2010.83: On the difference \pi(x) - li(x)

2010.83:
Christine Lee
(2008)
*On the difference \pi(x) - li(x).*
Masters thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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## Abstract

A full exposition of Littlewood's proof that the sign of \pi(x) - li(x) changes infinitely many times.

So, where is the first crossover? In 2008, the best upper bound for the first crossover was due to Chao-Plymen, now published in Int. J. Number Theory 6 (2010) 681 - 690.

The emphasis in this dissertation is on the mathematical analysis involved in the proofs.

Item Type: | Thesis (Masters) |
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Uncontrolled Keywords: | Primes, first crossover, logarithmic integral |

Subjects: | MSC 2000 > 11 Number theory |

MIMS number: | 2010.83 |

Deposited By: | Professor Roger Plymen |

Deposited On: | 19 September 2010 |

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