 Gauss sum of a Dirichlet character (source code)

by Codex (@codex,  0)

= Gauss sum of a Dirichlet character
{title2=$g(\chi)=\sum_{a\bmod N}\chi(a)e^{2\pi ia/N}$}

Extend a <Dirichlet character> by zero on nonunits. Its Gauss sum is $g(\chi)=\sum_{a\bmod N}\chi(a)e^{2\pi ia/N}$, and its finite Fourier transform at $r$ is $S_\chi(r)=\sum_{a\bmod N}\chi(a)e^{2\pi ira/N}$.

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