A continuous homomorphism of a group into the nonzero complex
numbers. A multiplicative character 
gives a group representation
on the one-dimensional space 
of complex numbers, where
the group representation action by 
is multiplication by 
. A multiplicative character is unitary
if it has absolute value 1 everywhere.
Multiplicative Character
See also
Grössencharakter, Unitary Multiplicative CharacterExplore with Wolfram|Alpha
References
Knapp, A. W. "Group Representations and Harmonic Analysis, Part II." Not. Amer. Math. Soc. 43, 537-549, 1996.Referenced on Wolfram|Alpha
Multiplicative CharacterCite this as:
Weisstein, Eric W. "Multiplicative Character." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MultiplicativeCharacter.html