Restriction of exponential sums to hypersurfaces

Abstract

We prove moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving estimates that are sharp with respect to the scale parameter $N$, apart from $N^{\epsilon }$ losses. In a few instances, we manage to remove these losses.

This new version also addresses the case d=5 for the moment curve