Vinogradov's mean value theorem via efficient congruencing

Trevor D. Wooley

doi:10.4007/annals.2012.175.3.12

Vinogradov's mean value theorem via efficient congruencing

Trevor D. Wooley^*

^*Corresponding author for this work

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

86 Citations (Scopus)

445 Downloads (Pure)

Abstract

We obtain estimates for Vinogradov's integral that for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring's problem holds for sums of 8 kth powers of natural numbers whenever s >= 2k² + 2k - 3.

Translated title of the contribution	Vinogradov's mean value theorem via efficient congruencing
Original language	English
Pages (from-to)	1575-1627
Number of pages	53
Journal	Annals of Mathematics
Volume	175
Issue number	3
DOIs	https://doi.org/10.4007/annals.2012.175.3.12
Publication status	Published - May 2012

Keywords

Waring's problem
Exponential sums
Hardy-Littlewood method

Access to Document

10.4007/annals.2012.175.3.12

ecvin20110711Accepted author manuscript, 562 KB

http://annals.math.princeton.edu/2012/175-3/p12

Handle.net

Persistent link

Cite this

@article{3079d292cb7d4e1d8e51976cb86f2929,

title = "Vinogradov's mean value theorem via efficient congruencing",

abstract = "We obtain estimates for Vinogradov's integral that for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring's problem holds for sums of 8 kth powers of natural numbers whenever s >= 2k2 + 2k - 3.",

keywords = "Waring's problem, Exponential sums, Hardy-Littlewood method",

author = "Wooley, {Trevor D.}",

year = "2012",

month = may,

doi = "10.4007/annals.2012.175.3.12",

language = "English",

volume = "175",

pages = "1575--1627",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Princeton University Press",

number = "3",

}

TY - JOUR

T1 - Vinogradov's mean value theorem via efficient congruencing

AU - Wooley, Trevor D.

PY - 2012/5

Y1 - 2012/5

N2 - We obtain estimates for Vinogradov's integral that for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring's problem holds for sums of 8 kth powers of natural numbers whenever s >= 2k2 + 2k - 3.

AB - We obtain estimates for Vinogradov's integral that for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring's problem holds for sums of 8 kth powers of natural numbers whenever s >= 2k2 + 2k - 3.

KW - Waring's problem

KW - Exponential sums

KW - Hardy-Littlewood method

U2 - 10.4007/annals.2012.175.3.12

DO - 10.4007/annals.2012.175.3.12

M3 - Article (Academic Journal)

SN - 0003-486X

VL - 175

SP - 1575

EP - 1627

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 3

ER -

Vinogradov's mean value theorem via efficient congruencing

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this