Dirichlet’n karakteristika

Olkoon ${\displaystyle A}$ polynomirengas ja ${\displaystyle m\in A}$ alkio, jonka aste on positiivinen. Dirichlet'n karakteri modulo ${\displaystyle m}$ on kuvaus ${\displaystyle \chi :A\to \mathbb {C} }$ jolle

• ${\displaystyle \chi (a+bm)=\chi (a)}$ kaikilla ${\displaystyle a,b\in A}$.
• ${\displaystyle \chi (a)\chi (b)=\chi (ab)}$ kaikilla ${\displaystyle a,b\in A}$.
• ${\displaystyle \chi (a)\neq 0}$ jos ja vain jos ${\displaystyle (a,m)=1}$.

• Michael Rosen: Number Theory in Function Fields, Springer, 2002.