ON WARING'S PROBLEM: TWO SQUARES, TWO CUBES AND TWO SIXTH POWERS

Trevor D. Wooley

doi:10.1093/qmath/hat007

ON WARING'S PROBLEM: TWO SQUARES, TWO CUBES AND TWO SIXTH POWERS

Trevor D. Wooley^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

We investigate the number of representations of a large positive integer as the sum of two squares, two positive integral cubes and two sixth powers, showing that the anticipated asymptotic formula fails for at most O ((log X)(3+epsilon)) positive integers not exceeding X.

Original language	English
Pages (from-to)	305-317
Number of pages	13
Journal	Quarterly Journal of Mathematics
Volume	65
Issue number	1
DOIs	https://doi.org/10.1093/qmath/hat007
Publication status	Published - Mar 2014

Keywords

SLIM EXCEPTIONAL SETS
RATIONAL-POINTS
SURFACES
DENSITY
SUMS

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title = "ON WARING'S PROBLEM: TWO SQUARES, TWO CUBES AND TWO SIXTH POWERS",

abstract = "We investigate the number of representations of a large positive integer as the sum of two squares, two positive integral cubes and two sixth powers, showing that the anticipated asymptotic formula fails for at most O ((log X)(3+epsilon)) positive integers not exceeding X.",

keywords = "SLIM EXCEPTIONAL SETS, RATIONAL-POINTS, SURFACES, DENSITY, SUMS",

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

year = "2014",

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AB - We investigate the number of representations of a large positive integer as the sum of two squares, two positive integral cubes and two sixth powers, showing that the anticipated asymptotic formula fails for at most O ((log X)(3+epsilon)) positive integers not exceeding X.

KW - SLIM EXCEPTIONAL SETS

KW - RATIONAL-POINTS

KW - SURFACES

KW - DENSITY

KW - SUMS

U2 - 10.1093/qmath/hat007

DO - 10.1093/qmath/hat007

M3 - Article (Academic Journal)

SN - 0033-5606

VL - 65

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EP - 317

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 1

ER -

ON WARING'S PROBLEM: TWO SQUARES, TWO CUBES AND TWO SIXTH POWERS

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Keywords

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