On Restriction Estimates for the Zero Radius Sphere over Finite Fields

Abstract

Abstract In this paper, we completely solve 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 the previous result of the first and second authors significantly.