Definition:Character (Number Theory)

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Let $\left({G, +}\right)$ be a finite abelian group.

Let $\left({\C_{\ne 0}, \times}\right)$ be the multiplicative group of complex numbers.

A character of $G$ is a group homomorphism:

$\chi: G \to \C_{\ne 0}$

Also see

In algebra, character refers to the trace of a representation of $G$.

This generalizes the number theorist's definition above.