In the analytic normalization, the functional equation relates $s$ to $1-s$ and the
**critical strip** is the open strip $\{ s \in {\mathbb C}: 0 < \Re(s) < 1 \}$.

In the arithmetic normalization, the functional equation relates $s$ to $1 + w - s$,
where $w$ is the motivic weight of the L-function,
and the
**critical strip** is the open strip $\{ s \in {\mathbb C}: w/2 < \Re(s) < w/2 + 1 \}$.

In either normalization, the Dirichlet series and Euler product converge absolutely to the right of the critical strip, and so the L-function does not vanish there. Therefore all nontrivial zeros of the L-function lie in (the closure of) the critical strip.

**Knowl status:**

- Review status: reviewed
- Last edited by Stephan Ehlen on 2019-04-30 13:02:18

**Referred to by:**

**History:**(expand/hide all)

- 2019-04-30 13:02:18 by Stephan Ehlen (Reviewed)
- 2019-04-30 12:55:33 by David Farmer (Reviewed)
- 2019-04-30 12:52:50 by David Farmer
- 2018-12-13 14:15:53 by Alex J. Best (Reviewed)

**Differences**(show/hide)