Improved discrete restriction for the parabola

TL;DR

This paper establishes a new bound on the discrete restriction constant for the parabola over the p-adic numbers, improving understanding of restriction phenomena in harmonic analysis.

Contribution

It introduces an improved discrete restriction estimate for the parabola over _p, leveraging ideas from Guth-Maldague-Wang.

Findings

Discrete restriction constant is bounded by O_{\u03b5}(( M)^{2+})

Advances the understanding of restriction estimates in harmonic analysis over _p

Provides new techniques inspired by Guth-Maldague-Wang

Abstract

Using ideas from Guth-Maldague-Wang and working over $\mathbb{Q}_p$, we show that the discrete restriction constant for the parabola is $O_{\varepsilon}((\log M)^{2 + \varepsilon})$.