Character Orthogonality
The orthogonality relations for characters of a finite group transfer to Dirichlet characters. If we fix a character χ modulo n then the sum
unless χ is principal, in which case the sum is φ(n). Similarly, if we fix a residue class a modulo n and sum over all characters we have
unless a=1 in which case the sum is φ(n). We deduce that any periodic function with period n supported on the residue classes prime to n is a linear combination of Dirichlet characters.
Read more about this topic: Dirichlet Character
Famous quotes containing the word character:
“The serial number of a human specimen is the face, that accidental and unrepeatable combination of features. It reflects neither character nor soul, nor what we call the self. The face is only the serial number of a specimen.”
—Milan Kundera (b. 1929)