The complex functions
\[
\Gamma_\R(s) := \pi^{-s/2}\Gamma(s/2)\qquad\text{and}\qquad \Gamma_\C(s):= 2(2\pi)^{-s}\Gamma(s)
\]
that appear in the functional equation of an L-function are known as **gamma factors**. Here $\Gamma(s):=\int_0^\infty e^{-t}t^{s-1}dt$ is Euler's gamma function.

The gamma factors satisfy $ \Gamma_\C(s) = \Gamma_\R(s) \Gamma_\R(s + 1) $ and can also be viewed as “missing” factors of the Euler product of an L-function corresponding to (real or complex) archimedean places.

**Knowl status:**

- Review status: reviewed
- Last edited by Edgar Costa on 2019-07-22 13:12:08

**Referred to by:**

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

- 2019-07-22 13:12:08 by Edgar Costa (Reviewed)
- 2019-06-05 16:37:58 by Andrew Sutherland (Reviewed)
- 2019-04-30 19:21:29 by Andrew Sutherland (Reviewed)
- 2019-04-30 19:21:19 by Andrew Sutherland
- 2019-04-30 19:20:20 by Andrew Sutherland
- 2019-02-22 16:43:02 by Andrew Sutherland (Reviewed)
- 2018-05-24 14:20:10 by John Cremona (Reviewed)

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