A bilinear proof of decoupling for the cubic moment curve

Abstract

Using a bilinear method that is inspired by the method of efficient congruencing of Wooley [Woo16], we prove a sharp decoupling inequality for the moment curve in ${\mathbb{R}}^3$.

arXiv comment28 pages; revised version incorporating referee comments

References in corpus (6)

• The cubic case of the main conjecture in Vinogradov's mean value theorem
• Nested efficient congruencing and relatives of Vinogradov's mean value theorem
• A short proof of the multilinear Kakeya inequality
• Decoupling for moment manifolds associated to Arkhipov--Chubarikov--Karatsuba systems
• The Cubic Case of Vinogradov's Mean Value Theorem --- A Simplified Approach to Wooley's "Efficient Congruencing"
• Effective $l^2$ decoupling for the parabola

Cited by in corpus (4)

• Decoupling for moment manifolds associated to Arkhipov--Chubarikov--Karatsuba systems
• Decoupling for two quadratic forms in three variables: a complete characterization
• Decoupling for fractal subsets of the parabola
• Supercritical discrete restriction estimates for forms in many variables