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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.

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