Number Theoretic Character

A number theoretic character, also called a Dirichlet character (because Dirichlet first introduced them in his famous proof that every arithmetic progression with relatively prime initial term and common difference contains infinitely many primes), modulo  is a complex function  for positive integer  such that

			(1)
			(2)
			(3)

for all , and

(4)

if .  can only assume values which are  roots of unity, where  is the totient function.

Number theoretic characters are implemented in the Wolfram Language as DirichletCharacter[k, j, n], where  is the modulus and  is the index.