
\documentclass{article}


\begin{document}

\begin{rawhtml}
<h1 align=center> Salem's criterion
</h1>
\end{rawhtml}


R. Salem [
\begin{rawhtml}
<a href="http://www.ams.org/msnmain?fn=130&s1=14_727a&pg1=MR">MR 14,727a</a>
\end{rawhtml}] proved that the 
non-vanishing of $\zeta(s)$ on the 
$\sigma$ --line is equivalent to the completeness in 
$L^1(0,\infty)$ of $\{k_\sigma(\lambda x),\ \lambda>0\}$ where
$$ k_\sigma(x) =\frac{x^{\sigma-1}}{e^x+1}.$$\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}

