Hasse-Davenport Relation
Let 
be a Finite Field with 
elements, and let 
be a Field containing such that
. Let 
be a nontrivial Multiplicative Character of and 
acharacter of . Then
where
is a Gaussian Sum.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.
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