# Principal character

From Encyclopedia of Mathematics

*Dirichlet principal character*

The arithmetic character $\chi_0$ defined by the condition $$ \chi_0(n) = \begin{cases} 1, & (n,D) = 1, \\ 0 & (n,D)>1. \end{cases} $$ where $D$ is a given natural number. Principal characters serve to define the concepts of primitive and imprimitive characters (cf. Dirichlet character).

**How to Cite This Entry:**

Principal character.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Principal_character&oldid=36154

This article was adapted from an original article by N.G. Chudakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article