Lee, Christine (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) |
|---|---|
| Uncontrolled Keywords: | Primes, first crossover, logarithmic integral |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory |
| Depositing User: | Professor Roger Plymen |
| Date Deposited: | 19 Sep 2010 |
| Last Modified: | 20 Oct 2017 14:12 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1524 |
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