Let be a Finite Field with elements, and let be a Field containing such that
. Let be a nontrivial Multiplicative Character of and
a
character of . Then
See also Gaussian Sum, Multiplicative Character
References
Ireland, K. and Rosen, M. ``A Proof of the Hasse-Davenport Relation.''
§11.4 in A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 162-165, 1990.