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The degree of an L-function is the number $J + 2K$ of Gamma factors occurring in its functional equation

\[ \Lambda(s) := N^{s/2} \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k) \cdot L(s) = \varepsilon \overline{\Lambda}(1-s). \]

The degree appears as the first component of the Selberg data of $L(s).$ In all known cases it is the degree of the polynomial of the inverse of the Euler factor at any prime not dividing the conductor.

Knowl status:
  • Review status: beta
  • Last edited by Christelle Vincent on 2015-09-16 20:47:29.077000