Formula:DLMF:25.15:E9

<< Formula:DLMF:25.15:E8

formula in Dirichlet L-functions

Formula:DLMF:25.15:E10 >>

${\displaystyle{\displaystyle{\displaystyle L\left(1,\chi\right)\neq 0\text{\quad if\quad}\chi\neq-1}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\chi_{1}}}}$ is the principal character~${\displaystyle{\displaystyle{\displaystyle\pmod{k}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle L}}}$ : Dirichlet ${\displaystyle{\displaystyle{\displaystyle L}}}$-function : http://dlmf.nist.gov/25.15#E1

Bibliography

Equation (9), Section 25.15 of DLMF.

URL links

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<< Formula:DLMF:25.15:E8

formula in Dirichlet L-functions

Formula:DLMF:25.15:E10 >>