
\documentclass{article}


\begin{document}

\begin{rawhtml}
<h1 align=center> More accurate estimates
</h1>
\end{rawhtml}

 

The Riemann hypothesis is equivalent to the following statement.

$$
\pi (x) -li (x) = O( \sqrt{x} \log x),
$$
(von Koch, Acta Mathematica 24 (1901), 159-182).

L.Schoenfeld [\begin{rawhtml}56 \#15581b\end{rawhtml}] gave in 1976 a numerically explicit version of this equivalent form :
$$
|\pi (x) -li (x)| \leq \frac{\sqrt{x}\log x}{8\pi}, \quad x \geq 2657.
$$
\begin{rawhtml}
<p> <br>
<hr>
<p> <br>
Back to the 
<a href="http://www.aimath.org/WWN/rh/"> main index</a> 
for The Riemann Hypothesis.
\end{rawhtml}

\end{document}

