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Updating the error term in the prime number theorem

Trudgian, Tim S.

Description

An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, the third to a conjecture by Pomerance and the fourth to an inequality studied by Ramanujan.

CollectionsANU Research Publications
Date published: 2015-01-08
Type: Journal article
URI: http://hdl.handle.net/1885/14913
Source: The Ramanujan Journal
DOI: 10.1007/s11139-014-9656-6

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