You are here: MIMS > EPrints
MIMS EPrints

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.

Full text available as:

PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
303 Kb

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 2000 > 11 Number theory
MIMS number:2010.83
Deposited By:Professor Roger Plymen
Deposited On:19 September 2010

Download Statistics: last 4 weeks
Repository Staff Only: edit this item