Tim Trudgian
Published 2014-01-13, updated 2014-10-17Version 2
An improved estimate is given for $|\theta(x) -x|$, where $\theta(x) = \sum_{p\leq x} \log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the third to a conjecture by C. Pomerance.
Comments: I wish to thank MG Johnson, RJ Harris, PM Siddle, and NM Lyon, all of whom enabled me to work two extra days on this article; 13 pages; to appear in Ramanujan J
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