On restriction estimates for the zero radius sphere over finite fields

TL;DR

This paper completely solves the $L^2 o L^r$ extension conjecture for the zero radius sphere over finite fields and improves the sharp $L^p o L^4$ extension estimates for non-zero radii spheres, advancing the understanding of restriction phenomena in finite field settings.

Contribution

The paper provides a complete solution to the extension conjecture for zero radius spheres and improves existing estimates for non-zero radii spheres over finite fields.

Findings

Complete solution to the $L^2 o L^r$ extension conjecture for zero radius spheres.

Sharp $L^p o L^4$ extension estimates for non-zero radii spheres.

Significant improvement over previous bounds for sphere extension estimates.

Abstract

In this paper, we solve completely the $L^2\to L^r$ extension conjecture for the zero radius sphere over finite fields. We also obtain the sharp $L^p\to L^4$ extension estimate for non-zero radii spheres over finite fields, which improves significantly the previous result of the first and second listed authors.