Dirichlet character

English

Noun

1. Template:Lb A complex-valued arithmetic function $\chi :\mathbb{Z}\to ℂ$ that satisfies the following conditions for some positive integer $m$ and all integers $a$ and $b$:

   1)   $\chi (ab)=\chi (a)\chi (b);$  

   2)   $\chi (a)\{\begin{array}{cc}=0& \text{if }\gcd (a,m)>1\\ \ne 0& \text{if }\gcd (a,m)=1.\end{array}$ (gcd is the greatest common divisor)

   3)   $\chi (a+m)=\chi (a)$.