The *critical line* is the line of symmetry in the
functional equation of the -function.
In the usual normalization the functional equation associates
to , so the critical line is
.

In the usual normalization the Dirichlet series and the Euler product
converge absolutely for The functional equation
maps to . The remaining region,
is known as the *critical strip*.

By the Euler product there are no zeros in , and by the functional equation there are only trivial zeros in . 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.

Back to the
main index
for The Riemann Hypothesis.