# Updating the error term in the prime number theorem

@article{Trudgian2014UpdatingTE,
title={Updating the error term in the prime number theorem},
author={Tim Trudgian},
journal={The Ramanujan Journal},
year={2014},
volume={39},
pages={225-234}
}
• T. Trudgian
• Published 2014
• Mathematics
• The Ramanujan Journal
An improved estimate is given for $$|\theta (x) -x|$$|θ(x)-x|, where $$\theta (x) = \sum _{p\le x} \log p$$θ(x)=∑p≤xlogp. 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.
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