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<h1 align=center> Critical line and critical strip
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The {\it critical line} is the line of symmetry in the 
\begin{rawhtml}<a href="../69a">functional equation</a>\end{rawhtml} of the $L$-function.
In the usual normalization the functional equation associates
$s$ to $1-s$, so the critical line is $\sigma=\frac12$.

In the usual normalization the Dirichlet series and the Euler product
converge absolutely for   The functional equation
maps $\sigma>1$ to $\sigma<0$.  The remaining region, 
$0<\sigma<1$ is known as the {\it critical strip}.

By the Euler product there are no zeros in $\sigma>1$, and by the 
functional equation there are only trivial zeros in $\sigma<0$.
So all of the nontrivial zeros are in the critical strip,
and the Riemann Hypothesis asserts that the nontrivial zeros
are actually on the critical line.
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Back to the 
<a href="http://www.aimath.org/WWN/rh/"> main index</a> 
for The Riemann Hypothesis.
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