Introduction to Analytic Number Theory
《Introduction to Analytic Number Theory》 · 第 138 页 · Section 6.6「Dirichlet characters」，Definition
For each character $f$ of the group of reduced residue classes modulo $k$ we define an arithmetical function $\chi$ by $\chi(n)=f(n)$ if $(n,k)=1$ and $\chi(n)=0$ if $(n,k)>1$. The function $\chi$ is called a Dirichlet character modulo $k$.