Let 
be a finite field with 
elements, and let 
be a field containing 
such that ![[F_s:F]=s](/images/equations/Hasse-DavenportRelation/Inline5.svg)
. Let 
be a nontrivial multiplicative
character of 
and 
a character of 
. Then
 |
where 
is a Gaussian sum.
Hasse-Davenport Relation
See also
Gaussian Sum, Multiplicative CharacterExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Hasse-Davenport RelationCite this as:
Weisstein, Eric W. "Hasse-Davenport Relation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hasse-DavenportRelation.html