Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums

Scott T. Parsell; Sean M. Prendiville; Trevor D. Wooley

doi:10.1007/s00039-013-0242-7

Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums

Scott T. Parsell^*, Sean M. Prendiville, Trevor D. Wooley

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

28 Citations (Scopus)

Abstract

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

Original language	English
Pages (from-to)	1962-2024
Number of pages	63
Journal	Geometric and Functional Analysis
Volume	23
Issue number	6
Early online date	6 Jul 2013
DOIs	https://doi.org/10.1007/s00039-013-0242-7
Publication status	Published - Dec 2013

Keywords

VALUE THEOREM
POINTS

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@article{9a167205edd64900b156b564d1892d46,

title = "Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums",

abstract = "We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.",

keywords = "VALUE THEOREM, POINTS",

author = "Parsell, {Scott T.} and Prendiville, {Sean M.} and Wooley, {Trevor D.}",

year = "2013",

month = dec,

doi = "10.1007/s00039-013-0242-7",

language = "English",

volume = "23",

pages = "1962--2024",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Springer International Publishing AG",

number = "6",

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TY - JOUR

T1 - Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums

AU - Parsell, Scott T.

AU - Prendiville, Sean M.

AU - Wooley, Trevor D.

PY - 2013/12

Y1 - 2013/12

N2 - We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

AB - We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

KW - VALUE THEOREM

KW - POINTS

U2 - 10.1007/s00039-013-0242-7

DO - 10.1007/s00039-013-0242-7

M3 - Article (Academic Journal)

SN - 1016-443X

VL - 23

SP - 1962

EP - 2024

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 6

ER -

Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums

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Keywords

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