Sharper Bounds for the Chebyshev function $\theta(x)$
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2020
- DOI:
- 10.48550/arXiv.2002.11068
- arXiv:
- arXiv:2002.11068
- Bibcode:
- 2020arXiv200211068B
- Keywords:
-
- Mathematics - Number Theory
- E-Print:
- 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