On the difference \pi(x) - li(x)

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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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: http://eprints.maths.manchester.ac.uk/id/eprint/1524

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