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

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

doi:10.1112/mtk.12231

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

Brian Cook, Kevin Hughes, Zane Kun Li^*, Akshat Mudgal, Olivier Robert, Po Lam Yung

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Article number	e12231
Journal	Mathematika
Volume	70
Issue number	1
DOIs	https://doi.org/10.1112/mtk.12231
Publication status	Published - 12 Dec 2023

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title = "A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem",

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.",

author = "Brian Cook and Kevin Hughes and Li, \{Zane Kun\} and Akshat Mudgal and Olivier Robert and Yung, \{Po Lam\}",

note = "Publisher Copyright: {\textcopyright} 2023 The Authors. Mathematika is copyright {\textcopyright} University College London and published by the London Mathematical Society on behalf of University College London.",

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AU - Hughes, Kevin

AU - Li, Zane Kun

AU - Mudgal, Akshat

AU - Robert, Olivier

AU - Yung, Po Lam

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Y1 - 2023/12/12

N2 - 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.

AB - 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.

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U2 - 10.1112/mtk.12231

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M3 - Article

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JO - Mathematika

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

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