DirichletCharacter

DirichletCharacter[k,j,n]

gives the Dirichlet character with modulus k and index j.

Details

  • 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.

Examples

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Basic Examples  (2)

A basic Dirichlet character:

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All the modulo 7 characters:

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Plot them:

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Scope  (3)

Applications  (5)

Properties & Relations  (11)

See Also

DirichletL  EulerPhi  PrimitiveRoot  JacobiSymbol

Introduced in 2008
(7.0)