A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem

Cook, Brian; Hughes, Kevin; Li, Zane Kun; Mudgal, Akshat; Robert, Olivier; Yung, Po‐Lam

Abstract

We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely solution counting in older partial progress on Vinogradov's mean value theorem corresponds to in Fourier decoupling theory.

• Journal Article Type: Article
• Acceptance Date: Oct 12, 2023
• Online Publication Date: Nov 12, 2023
• Publication Date: 2024-01
• Deposit Date: Jan 10, 2024
• Journal: Mathematika
• Print ISSN: 0025-5793
• Electronic ISSN: 2041-7942
• Publisher: University College London, Faculty of Mathematical and Physical Sciences, Department of Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 70
• Issue: 1
• Article Number: e12231
• DOI: https://doi.org/10.1112/mtk.12231
• Public URL: http://researchrepository.napier.ac.uk/Output/3389210