A sharp $L^{10}$ decoupling for the twisted cubic

TL;DR

This paper establishes a precise decoupling inequality for the moment curve in three-dimensional space, advancing understanding of harmonic analysis and decoupling theory.

Contribution

It introduces a sharp $l^{10}(L^{10})$ decoupling result for the twisted cubic, utilizing a novel two-step decoupling approach and new incidence estimates.

Findings

Proves a sharp decoupling inequality for the moment curve in $\



Abstract

We prove a sharp $l^{10}(L^{10})$ decoupling for the moment curve in $\mathbb{R}^3$. The proof involves a two-step decoupling combined with new incidence estimates for planks, tubes and plates.