
\documentclass{article}


\begin{document}

\begin{rawhtml}
<h1 align=center> Bombieri's refinement
</h1>
\end{rawhtml}

 
Bombieri [\begin{rawhtml}1 841 692\end{rawhtml}]has given the following version of Weil's criterion:
 The Riemann Hypothesis holds  if and only if
$$\sum_{\rho}\hat{g}(\rho) \hat{\overline{g}}(1-\rho)>0$$
for every complex-valued $g(x)\in C_0^\infty(0,\infty)$ 
which is not identically 0, where
$$\hat{g}(s)=\int_0^\infty g(x)x^{s-1}~dx$$
\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}

