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arXiv · 2002.11068

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

Samuel Broadbent·Habiba Kadiri·Allysa Lumley·Nathan Ng·Kirsten Wilk
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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.

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Samuel Broadbent, Habiba Kadiri, Allysa Lumley, Nathan Ng, Kirsten Wilk. 2020-02-25. Sharper Bounds for the Chebyshev function $\theta(x)$. https://arxiv.org/abs/2002.11068

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