View source for Principal character

''Dirichlet principal character''

The arithmetic character <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074650/p0746501.png" /> defined by the condition

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074650/p0746502.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074650/p0746503.png" /> is a given natural number. Principal characters serve to define the concepts of primitive and imprimitive characters (cf. [[Dirichlet character|Dirichlet character]]).