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

TL;DR

This paper advances the understanding of discrete Fourier restriction estimates on higher-dimensional spheres by improving the exponent bounds for dimensions four and above.

Contribution

It provides a sharper exponent bound for the discrete Fourier restriction problem on the n-dimensional sphere, enhancing previous results for n ≥ 4.

Findings

Improved the exponent from 2(n+1)/(n-3) to 2n/(n-3) for n ≥ 4.

Established tighter bounds for discrete Fourier restriction estimates.

Contributed to the theoretical understanding of Fourier analysis on spheres.

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 $n\ge 4$.