A light-weight version of Waring's problem

TD Wooley

A light-weight version of Waring's problem

TD Wooley^*

^*Corresponding author for this work

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

Abstract

An asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.

Translated title of the contribution	A light-weight version of Waring's problem
Original language	English
Pages (from-to)	303 - 316
Number of pages	14
Journal	Journal of the Australian Mathematical Society
Volume	76 (3)
Publication status	Published - Jun 2004

Bibliographical note

Publisher: Australian Mathematics Publ Assoc Ltd

Keywords

Waring's problem
applications of the Hardy-Littlewood method
THEOREM

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title = "A light-weight version of Waring's problem",

abstract = "An asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.",

keywords = "Waring's problem, applications of the Hardy-Littlewood method, THEOREM",

author = "TD Wooley",

note = "Publisher: Australian Mathematics Publ Assoc Ltd",

year = "2004",

month = jun,

language = "English",

volume = "76 (3)",

pages = "303 -- 316",

journal = "Journal of the Australian Mathematical Society",

issn = "1446-7887",

publisher = "Cambridge University Press",

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T1 - A light-weight version of Waring's problem

AU - Wooley, TD

N1 - Publisher: Australian Mathematics Publ Assoc Ltd

PY - 2004/6

Y1 - 2004/6

N2 - An asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.

AB - An asymptotic formula is established for the number of representations of a large integer as the sum of kth powers of natural numbers, in which each representation is counted with a homogeneous weight that de-emphasises the large solutions. Such an asymptotic formula necessarily fails when this weight is excessively light.

KW - Waring's problem

KW - applications of the Hardy-Littlewood method

KW - THEOREM

M3 - Article (Academic Journal)

SN - 1446-7887

VL - 76 (3)

SP - 303

EP - 316

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

ER -

A light-weight version of Waring's problem

Abstract

Bibliographical note

Keywords

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