= Completed Dirichlet L-function
{title2=$\Lambda(s,\chi)=(q/\pi)^{(s+a)/2}\Gamma((s+a)/2)L(s,\chi)$}
For a primitive nonprincipal <Dirichlet character>, the theta Mellin integral makes this an <entire function> satisfying $\Lambda(s,\chi)=\varepsilon_\chi\Lambda(1-s,\overline\chi)$. The gamma <poles> cancel the <trivial zeros of a Dirichlet L-function>. For the <principal Dirichlet character> whose <conductor of a Dirichlet character> is one the completion is <meromorphic>, with <poles> at zero and one.
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