##  [Dirichlet Character](/dirichlet-character) 

  ##  [Dirichlet Character](https://puremath.quantumdictionary.io/dirichlet-character-0) 

  

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Definition

A Dirichlet character modulo N is a completely multiplicative arithmetic function χ: Z -> C that is periodic of period N, vanishes on integers not coprime to N, and factors through the unit group (Z/NZ)^× via a group homomorphism to C^×.