Wolfram Language & System 10.3 (2015)|Legacy Documentation

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gives the Dirichlet character with modulus k and index j.


  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • DirichletCharacter[k,j,n] picks a particular ordering for possible Dirichlet characters modulo k.
  • There are ϕ distinct Dirichlet characters for a given modulus k, as labeled by the index j. Different conventions can give different orderings for the possible characters.
  • DirichletCharacter[k,j,n] is periodic in n with period k.
  • DirichletCharacter[k,j,n] is zero when n is not coprime to k.
  • DirichletCharacter[k,j,n] is a multiplicative function in n.
Introduced in 2008