ON WARING'S PROBLEM: THREE CUBES AND A MINICUBE

Joerg Bruedern; Trevor D. Wooley

doi:10.1215/00277630-2010-012

ON WARING'S PROBLEM: THREE CUBES AND A MINICUBE

Joerg Bruedern^*, Trevor D. Wooley

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

We establish that almost all natural numbers n are the sum of four cubes of positive integers, one of which is no larger than n(5/36). The proof makes use of an estimate for a certain eighth moment of cubic exponential sums, restricted to minor arcs only, of independent interest.

Original language	English
Pages (from-to)	59-91
Number of pages	33
Journal	Nagoya Mathematical Journal
Volume	200
DOIs	https://doi.org/10.1215/00277630-2010-012
Publication status	Published - Dec 2010

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SUMS

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title = "ON WARING'S PROBLEM: THREE CUBES AND A MINICUBE",

abstract = "We establish that almost all natural numbers n are the sum of four cubes of positive integers, one of which is no larger than n(5/36). The proof makes use of an estimate for a certain eighth moment of cubic exponential sums, restricted to minor arcs only, of independent interest.",

keywords = "SUMS",

author = "Joerg Bruedern and Wooley, {Trevor D.}",

year = "2010",

month = dec,

doi = "10.1215/00277630-2010-012",

language = "English",

volume = "200",

pages = "59--91",

journal = "Nagoya Mathematical Journal",

issn = "0027-7630",

publisher = "Nagoya University",

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TY - JOUR

T1 - ON WARING'S PROBLEM: THREE CUBES AND A MINICUBE

AU - Bruedern, Joerg

AU - Wooley, Trevor D.

PY - 2010/12

Y1 - 2010/12

N2 - We establish that almost all natural numbers n are the sum of four cubes of positive integers, one of which is no larger than n(5/36). The proof makes use of an estimate for a certain eighth moment of cubic exponential sums, restricted to minor arcs only, of independent interest.

AB - We establish that almost all natural numbers n are the sum of four cubes of positive integers, one of which is no larger than n(5/36). The proof makes use of an estimate for a certain eighth moment of cubic exponential sums, restricted to minor arcs only, of independent interest.

KW - SUMS

U2 - 10.1215/00277630-2010-012

DO - 10.1215/00277630-2010-012

M3 - Article (Academic Journal)

SN - 0027-7630

VL - 200

SP - 59

EP - 91

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

ER -

ON WARING'S PROBLEM: THREE CUBES AND A MINICUBE

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