Exercise 11, § 1

Tag 02KN, permanent. Cite it as [Bourbaki, Tag 02KN].

Spectral Theories, II, p. 265

Let $G$ be a finite abelian group and $d$ an integer $\geqslant 1$ . Prove that for every $x\in G$ and every $\chi \in \widehat{G}$ , one has

\sum_{y\in G}\chi (y) =\sum_{\eta\in G}\eta (x)

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