The **root number** of an Artin representation $\rho$,
also called the **sign**, is the constant $W(\rho)$ appearing in the
functional equation
of the associated L-function, i.e. the complex number $W(\rho)$ of absolute value $1$ such that $\Lambda(s,\rho)=W(\rho)\Lambda(1-s,\overline{\rho})$. It can be expressed as a product of local root numbers.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by David Farmer on 2012-06-28 08:57:15

**Referred to by:**

- test.text
- lmfdb/artin_representations/main.py (line 542)
- lmfdb/artin_representations/templates/artin-representation-galois-orbit.html (line 14)
- lmfdb/artin_representations/templates/artin-representation-search.html (line 21)
- lmfdb/artin_representations/templates/artin-representation-show.html (line 14)
- lmfdb/number_fields/templates/nf-show-field.html (line 265)

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

- 2012-06-28 08:57:15 by David Farmer (Reviewed)