Improved estimates for the discrete Fourier restriction to the higher dimensional sphere

Abstract

We improve the exponent for the discrete Fourier restriction to the $n$ dimensional sphere, from $p=\frac{2(n+1)}{n-3}$ to $p=\frac{2n}{n-3}$, when $n\ge 4$.

This paper is an improved version of an earlier draft by the second author. It covers also dimensions four and five