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The critical line of an L-function is the line of symmetry of its functional equation.

In the analytic normalization, the functional equation relates $s$ to $1-s$ and the critical line is the line $\Re(s) = \frac12$.

In the arithmetic normalization, the functional equation relates $s$ to $1 + w - s$, where $w$ is the motivic weight. In that normalization the critical line is $\Re(s) = \frac{1+w}2$.

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• Review status: reviewed
• Last edited by David Farmer on 2019-04-30 12:46:53
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