Difference between revisions of "Principal character"
From Encyclopedia of Mathematics
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''Dirichlet principal character'' | ''Dirichlet principal character'' | ||
| − | The arithmetic 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 | + | where $D$ is a given natural number. Principal characters serve to define the concepts of primitive and imprimitive characters (cf. [[Dirichlet character]]). |
Latest revision as of 20:04, 9 January 2015
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=17215
Principal character. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_character&oldid=17215
This article was adapted from an original article by N.G. Chudakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article