Formula:DLMF:25.15:E2

<< Formula:DLMF:25.15:E1

formula in Dirichlet L-functions

Formula:DLMF:25.15:E3 >>

${\displaystyle{\displaystyle{\displaystyle L\left(s,\chi\right)=\prod_{p}\left(1-\frac{\chi(p)}{p^{s}}\right)^{-1}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\Re{s}>1}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle L}}}$ : Dirichlet ${\displaystyle{\displaystyle{\displaystyle L}}}$-function : http://dlmf.nist.gov/25.15#E1
${\displaystyle{\displaystyle{\displaystyle\Pi}}}$ : product : http://drmf.wmflabs.org/wiki/Definition:prod
${\displaystyle{\displaystyle{\displaystyle\Re{z}}}}$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation (2), Section 25.15 of DLMF.

URL links

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<< Formula:DLMF:25.15:E1

formula in Dirichlet L-functions

Formula:DLMF:25.15:E3 >>