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.
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- Last edited by Christelle Vincent on 2015-09-16 20:47:29
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- columns.lfunc_lfunctions.degree
- columns.lfunc_search.degree
- g2c.169.a.169.1.bottom
- intro
- intro.features
- intro.tutorial
- lfunction
- lfunction.euler_product
- lfunction.functional_equation
- lfunction.invariants
- lfunction.known_degree1
- lfunction.known_degree2
- lfunction.known_degree3
- lfunction.known_degree4
- lfunction.label
- lfunction.root_analytic_conductor
- lfunction.selbergdata
- lfunction.underlying_object
- rcs.cande.lfunction
- lmfdb/lfunctions/main.py (line 323)
- lmfdb/lfunctions/main.py (line 467)
- lmfdb/lfunctions/templates/Lfunction.html (line 76)
- lmfdb/lfunctions/templates/LfunctionNavigate.html (line 9)
- 2015-09-16 20:47:29 by Christelle Vincent (Reviewed)