Additive representation in short intervals, I: Waring's problems for cubes

J Brüdern; TD Wooley

doi:10.1112/S0010437X04001058

Additive representation in short intervals, I: Waring's problems for cubes

J Brüdern, TD Wooley

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Abstract

Estimates are established for the number of integers of size N, in intervals of size N-theta, that fail to admit a representation as the sum of s cubes (s = 5, 6). Thereby it is shown that almost all such integers are represented in the proposed manner. When s = 5 one may take theta = 10/21, and when s = 6 one may take any theta > 17/63. Similar such conclusions are also established for the related problem associated with the expected asymptotic formula.

Translated title of the contribution	Additive representation in short intervals, I: Waring's problems for cubes
Original language	English
Pages (from-to)	1197 - 1220
Number of pages	24
Journal	Compositio Mathematica
Volume	140 (5)
DOIs	https://doi.org/10.1112/S0010437X04001058
Publication status	Published - 1 Sept 2004

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Publisher: London Math Soc

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http://www.journals.cambridge.org/download.php?file=%2FCOM%2FCOM140_05%2FS0010437X04001058a.pdf&code=a3dfebdcc07f00820e7fa9d615b280fd

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abstract = "Estimates are established for the number of integers of size N, in intervals of size N-theta, that fail to admit a representation as the sum of s cubes (s = 5, 6). Thereby it is shown that almost all such integers are represented in the proposed manner. When s = 5 one may take theta = 10/21, and when s = 6 one may take any theta > 17/63. Similar such conclusions are also established for the related problem associated with the expected asymptotic formula.",

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AU - Wooley, TD

N1 - Publisher: London Math Soc

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Y1 - 2004/9/1

N2 - Estimates are established for the number of integers of size N, in intervals of size N-theta, that fail to admit a representation as the sum of s cubes (s = 5, 6). Thereby it is shown that almost all such integers are represented in the proposed manner. When s = 5 one may take theta = 10/21, and when s = 6 one may take any theta > 17/63. Similar such conclusions are also established for the related problem associated with the expected asymptotic formula.

AB - Estimates are established for the number of integers of size N, in intervals of size N-theta, that fail to admit a representation as the sum of s cubes (s = 5, 6). Thereby it is shown that almost all such integers are represented in the proposed manner. When s = 5 one may take theta = 10/21, and when s = 6 one may take any theta > 17/63. Similar such conclusions are also established for the related problem associated with the expected asymptotic formula.

U2 - 10.1112/S0010437X04001058

DO - 10.1112/S0010437X04001058

M3 - Article (Academic Journal)

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EP - 1220

JO - Compositio Mathematica

JF - Compositio Mathematica

ER -

Additive representation in short intervals, I: Waring's problems for cubes

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