  We prove essentially sharp bounds for the $L^p$ restriction of weighted Gauss
sums to monomial curves. Getting the $L^2$ upper bound combines the $TT^*$
method for matrices with the first and second derivative test for exponential
sums. The matching lower bound follows via constructive interference on short
blocks of integers, near the critical point of the phase function. This method
is used to make the broader point that restriction to hypersurfaces is really
sensitive to curvature. Our results here complement earlier results by the
author and Langowski.
