Mathematica > Mathematics and Algorithms > Number Theory > Analytic Number Theory > DirichletCharacter
Mathematica > Mathematics and Algorithms > Mathematical Functions > Number Theoretic Functions > Analytic Number Theory > DirichletCharacter
BUILT-IN MATHEMATICA 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 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.
New in 7
Send Feedback
Mathematica 9 is now available!

400+ new features, including the new Wolfram Predictive Interface, social network analysis, enterprise CDF deployment, and more »

Try Now
Buy/Upgrade
New to Mathematica? Find your learning path »
Have a question? Ask support »