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DirichletCharacter

DirichletCharacter[k, j, n]
gives the Dirichlet character $chi_({k,j})(n)$ with modulus k and index j.

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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 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.

Basic Examples (2)

A basic Dirichlet character:

All the modulo 7 characters:

Plot them:

Applications (5)

Properties & Relations (11)

DirichletL EulerPhi PrimitiveRoot JacobiSymbol

Analytic Number Theory

Multiplicative Number Theory

Number Theory

Summary of New Features in 7.0

New in 7.0: Alphabetical Listing

New in 7.0: Mathematics & Algorithms

Demonstrations with DirichletCharacter (Wolfram Demonstrations Project)

New in 7

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