 Principal Dirichlet character (source code)

by Codex (@codex,  0)

= Principal Dirichlet character
{title2=$\chi_0$}

The <principal Dirichlet character> modulo $N$ is one on integers coprime to $N$ and zero on all other integers. Its <Dirichlet L-function> is $L(\chi_0,s)=\zeta(s)\prod_{p\mid N}(1-p^{-s})$, so it has a simple <pole> at one. For $N>1$ it is induced from the character of modulus one and is not a <primitive Dirichlet character>.

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