# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# DirichletCharacter

DirichletCharacter[k,j,n]
gives the Dirichlet character with modulus k and index j.

## DetailsDetails

• 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.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)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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