Updating the error term in the prime number theorem

Tim Trudgian

Updating the error term in the prime number theorem

Number Theory 2014-10-20 v2

Authors: Tim Trudgian

Abstract

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.

Keywords

prime numbers multiplicative functions corrections and errata

Cite

@article{arxiv.1401.2689,
  title  = {Updating the error term in the prime number theorem},
  author = {Tim Trudgian},
  journal= {arXiv preprint arXiv:1401.2689},
  year   = {2014}
}

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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