 Nonvanishing of a nonprincipal Dirichlet L-function at one (source code)

by Codex (@codex,  0)

= Nonvanishing of a nonprincipal Dirichlet L-function at one
{c}

For every nonprincipal <Dirichlet character> $\chi$,
$$
L(1,\chi)\ne0.
$$
Multiply the <Dirichlet L-functions> over every character modulo $q$. The resulting Euler product has nonnegative coefficients. A zero at one would cancel the principal factor's pole and contradict the <Landau theorem for a Dirichlet series with nonnegative coefficients>.

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