Sharper Bounds for the Chebyshev function $\theta(x)$

Samuel Broadbent; Habiba Kadiri; Allysa Lumley; Nathan Ng; Kirsten Wilk

Sharper Bounds for the Chebyshev function $\theta(x)$

Number Theory 2021-01-29 v2

Authors: Samuel Broadbent , Habiba Kadiri , Allysa Lumley , Nathan Ng , Kirsten Wilk

Abstract

In this article, we provide explicit bounds for the prime counting function $\theta(x)$ in all ranges of $x$ . The bounds for the error term for $\theta (x)- x$ are of the shape $\epsilon x$ and $\frac{c_k x}{(\log x)^k}$ , for $k=1,\ldots,5$ . Tables of values for $\epsilon$ and $c_k$ are provided.

Cite

@article{arxiv.2002.11068,
  title  = {Sharper Bounds for the Chebyshev function $\theta(x)$},
  author = {Samuel Broadbent and Habiba Kadiri and Allysa Lumley and Nathan Ng and Kirsten Wilk},
  journal= {arXiv preprint arXiv:2002.11068},
  year   = {2021}
}

Comments

There is 41 page accompanying file to the main article which includes longer versions of Tables 8 to 15. This has the additional authors: Andrew Fiori and Josh Swidinsky

Sharper Bounds for the Chebyshev function $\theta(x)$

Abstract

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