show · character.dirichlet.modulus all knowls · up · search:

A Dirichlet character is a function χ:ZC\chi: \mathbb Z\to \mathbb C together with a positive integer qq, called the modulus of the character, such that χ\chi is completely multiplicative, i.e. χ(mn)=χ(m)χ(n)\chi(mn)=\chi(m)\chi(n) for all integers mm and nn, and χ\chi is periodic modulo qq, i.e. χ(n+q)=χ(n)\chi(n+q)=\chi(n) for all nn. If (n,q)>1(n,q)>1 then χ(n)=0\chi(n)=0, whereas if (n,q)=1(n,q)=1, then χ(n)\chi(n) is a root of unity.

Authors:
Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2012-06-26 14:36:51
Referred to by:
History: (expand/hide all)