Slim exceptional sets for sums of cubes

TD Wooley

Slim exceptional sets for sums of cubes

TD Wooley

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

23 Citations (Scopus)

Abstract

We investigate exceptional sets associated with various additive problems involving sums of cubes. By developing a method wherein an exponential sum over the set of exceptions is employed explicitly within the Hardy-Littlewood method, we are better able to exploit excess variables. By way of illustration, we show that the number of odd integers not divisible by 9, and not exceeding X, that fail to have a representation as the sum of 7 cubes of prime numbers, is O(X23/36+epsilon). For sums of eight cubes of prime numbers, the corresponding number of exceptional integers is O(X-11/(36+epsilon)).

Translated title of the contribution	Slim exceptional sets for sums of cubes
Original language	English
Pages (from-to)	417 - 448
Number of pages	32
Journal	Canadian Journal of Mathematics . Journal Canadien de Mathematiques
Volume	54 (2)
Publication status	Published - Apr 2002

Bibliographical note

Publisher: Canadian Mathematical Soc

Access to Document

http://journals.cms.math.ca/cgi-bin/vault/view/wooley1034

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title = "Slim exceptional sets for sums of cubes",

abstract = "We investigate exceptional sets associated with various additive problems involving sums of cubes. By developing a method wherein an exponential sum over the set of exceptions is employed explicitly within the Hardy-Littlewood method, we are better able to exploit excess variables. By way of illustration, we show that the number of odd integers not divisible by 9, and not exceeding X, that fail to have a representation as the sum of 7 cubes of prime numbers, is O(X23/36+epsilon). For sums of eight cubes of prime numbers, the corresponding number of exceptional integers is O(X-11/(36+epsilon)).",

author = "TD Wooley",

note = "Publisher: Canadian Mathematical Soc",

year = "2002",

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journal = "Canadian Journal of Mathematics . Journal Canadien de Mathematiques",

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AU - Wooley, TD

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PY - 2002/4

Y1 - 2002/4

N2 - We investigate exceptional sets associated with various additive problems involving sums of cubes. By developing a method wherein an exponential sum over the set of exceptions is employed explicitly within the Hardy-Littlewood method, we are better able to exploit excess variables. By way of illustration, we show that the number of odd integers not divisible by 9, and not exceeding X, that fail to have a representation as the sum of 7 cubes of prime numbers, is O(X23/36+epsilon). For sums of eight cubes of prime numbers, the corresponding number of exceptional integers is O(X-11/(36+epsilon)).

AB - We investigate exceptional sets associated with various additive problems involving sums of cubes. By developing a method wherein an exponential sum over the set of exceptions is employed explicitly within the Hardy-Littlewood method, we are better able to exploit excess variables. By way of illustration, we show that the number of odd integers not divisible by 9, and not exceeding X, that fail to have a representation as the sum of 7 cubes of prime numbers, is O(X23/36+epsilon). For sums of eight cubes of prime numbers, the corresponding number of exceptional integers is O(X-11/(36+epsilon)).

M3 - Article (Academic Journal)

VL - 54 (2)

SP - 417

EP - 448

JO - Canadian Journal of Mathematics . Journal Canadien de Mathematiques

JF - Canadian Journal of Mathematics . Journal Canadien de Mathematiques

SN - 0008-414X

ER -