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2010.102: On the positive region of \pi(x) - li(x)

2010.102: Stefanie Zegowitz (2010) On the positive region of \pi(x) - li(x). Other 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 (Other)
Uncontrolled Keywords:primes, logarithmic integral, first crossover
Subjects:MSC 2000 > 11 Number theory
MIMS number:2010.102
Deposited By:Professor Roger Plymen
Deposited On:06 December 2010

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