Dirichlet character

Common card · No. 384544

In analytic number theory and related branches of mathematics, a complex-valued arithmetic function χ : Z → C {\displaystyle \chi :\mathbb {Z} \rightarrow \mathbb {C} } is a Dirichlet character of modulus m {\displaystyle m} (where m {\displaystyle m} is a positive integer) if for all integers a {\displaystyle a} and b {\displaystyle b} : 1. χ ( a b ) = χ ( a ) χ ( b ) ; {\displaystyle \chi (ab)=\chi (a)\chi (b);} that is, χ {\displaystyle \chi } is completely multiplicative. 2....

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