A Gauss sum over a finite field combines a multiplicative character 
with a nontrivial additive character 
in the sum
 |
where 
is extended by zero at zero. For a
nontrivial 
,
its absolute value is 
. The normalized sum 
therefore lies on the unit
circle. A character of order 3 gives a cubic Gauss
sum. Quadratic exponential sums are treated as Gaussian sums. The additive-character
normalization matters when comparing first moments.
-Functions for Gauss and Jacobi Sums."