The asymptotic formulae in Waring's problem for cubes

J Brudern; TD Wooley

doi:10.1515/CRELLE.2010.071

The asymptotic formulae in Waring's problem for cubes

J Brudern
, TD Wooley

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

5 Citations (Scopus)

Abstract

Write R_s(n) for the number of representations of a natural number as the sum of s positive integral cubes. We investigate the higher moments of R_s(n), establishing asymptotic formulae for when s = 5 and h = 3, when s = 6 and h <28/5, and when s = 7 and h =12. Hitherto, such an asymptotic formula was available only when s =4 and h = 2.

Translated title of the contribution	The asymptotic formulae in Waring's problem for cubes
Original language	English
Pages (from-to)	1 - 23
Number of pages	23
Journal	Journal für die reine und angewandte Mathematik
Volume	647
DOIs	https://doi.org/10.1515/CRELLE.2010.071
Publication status	Published - Oct 2010

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Publisher: de Gruyter

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title = "The asymptotic formulae in Waring's problem for cubes",

abstract = "Write R\_s(n) for the number of representations of a natural number as the sum of s positive integral cubes. We investigate the higher moments of R\_s(n), establishing asymptotic formulae for when s = 5 and h = 3, when s = 6 and h <28/5, and when s = 7 and h =12. Hitherto, such an asymptotic formula was available only when s =4 and h = 2.",

author = "J Brudern and TD Wooley",

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doi = "10.1515/CRELLE.2010.071",

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T1 - The asymptotic formulae in Waring's problem for cubes

AU - Brudern, J

AU - Wooley, TD

N1 - Publisher: de Gruyter

PY - 2010/10

Y1 - 2010/10

N2 - Write R_s(n) for the number of representations of a natural number as the sum of s positive integral cubes. We investigate the higher moments of R_s(n), establishing asymptotic formulae for when s = 5 and h = 3, when s = 6 and h <28/5, and when s = 7 and h =12. Hitherto, such an asymptotic formula was available only when s =4 and h = 2.

AB - Write R_s(n) for the number of representations of a natural number as the sum of s positive integral cubes. We investigate the higher moments of R_s(n), establishing asymptotic formulae for when s = 5 and h = 3, when s = 6 and h <28/5, and when s = 7 and h =12. Hitherto, such an asymptotic formula was available only when s =4 and h = 2.

U2 - 10.1515/CRELLE.2010.071

DO - 10.1515/CRELLE.2010.071

M3 - Article (Academic Journal)

SN - 1435-5345

VL - 647

SP - 1

EP - 23

JO - Journal für die reine und angewandte Mathematik

JF - Journal für die reine und angewandte Mathematik

ER -

The asymptotic formulae in Waring's problem for cubes

Abstract

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