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arXiv · 1401.2689

Updating the error term in the prime number theorem

Tim Trudgian
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Abstract

An improved estimate is given for $|θ(x) -x|$, where $θ(x) = \sum_{p\leq x} \log p$. 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.

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Tim Trudgian. 2014-10-17. Updating the error term in the prime number theorem. https://arxiv.org/abs/1401.2689

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