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 $\Re(s) = \frac{1+w}2$.

**Authors:**

**Knowl status:**

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

**Referred to by:**

- intro.tutorial
- lfunction
- lfunction.central_point
- lfunction.riemann
- lfunction.zeros
- lfunction.zfunction
- rcs.rigor.lfunction.dirichlet
- rcs.rigor.lfunction.modular
- lmfdb/lfunctions/templates/Lfunction.html (line 253)
- lmfdb/lfunctions/templates/Lfunction.html (line 268)
- lmfdb/lfunctions/templates/cuspformGL2.html (line 22)

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

- 2019-04-30 12:46:53 by David Farmer (Reviewed)
- 2019-04-30 12:45:07 by David Farmer
- 2011-09-06 08:28:46 by Jennifer Beineke (Reviewed)

**Differences**(show/hide)