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The conductor of an L-function is the integer $N$ 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 conductor of an analytic L-function is the second component in the Selberg data. For a Dirichlet L-function associated with a primitive Dirichlet character, the conductor of the L-function is the same as the conductor of the character. For a primitive L-function associated with a cusp form $\phi$ on $GL(2)/\mathbb Q$, the conductor of the L-function is the same as the level of $\phi$.

In the literature, the word level is sometimes used instead of conductor.

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• Review status: reviewed
• Last edited by Christelle Vincent on 2015-09-16 18:40:07
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