Small cap decoupling for the moment curve in $\mathbb{R}^3$

TL;DR

This paper establishes precise small cap decoupling estimates for the moment curve in three-dimensional space, advancing understanding of exponential sums and their $L^p$ bounds.

Contribution

It provides sharp small cap decoupling results for the moment curve in $ extbf{R}^3$, motivated by conjectures on $L^p$ estimates for exponential sums.

Findings

Sharp small cap decoupling estimates proved for the moment curve in $ extbf{R}^3$

Results support conjectures on $L^p$ bounds for exponential sums

Methodology connects decoupling theory with exponential sum estimates

Abstract

We prove sharp small cap decoupling estimates for the moment curve in $\mathbb{R}^3$. Our formulation of the small caps is motivated by a conjecture about $L^p$ estimates for exponential sums from the small cap decoupling paper of Demeter, Guth, and Wang.