On Waring's problem for intermediate powers

Trevor D Wooley

doi:10.4064/aa8439-8-2016

On Waring's problem for intermediate powers

Trevor D Wooley

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Abstract

Let G(k) denote the least number s such that every suffciently large natural number is the sum of at most s positive integral kth powers. We show that G(7) ≤ 31, G(8) ≤ 39, G(9) ≤ 47, G(10) ≤ 55, G(11) ≤ 63, G(12) ≤ 72, G(13) ≤ 81, G(14) ≤ 90, G(15) ≤ 99, G(16) ≤ 108.

Original language	English
Pages (from-to)	241-247
Number of pages	7
Journal	Acta Arithmetica
Volume	176
Issue number	3
Early online date	29 Sept 2016
DOIs	https://doi.org/10.4064/aa8439-8-2016
Publication status	Published - 4 Nov 2016

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Polish Institute of Mathematics at https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/online/91775/on-waring-s-problem-for-intermediate-powers. Please refer to any applicable terms of use of the publisher.
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title = "On Waring's problem for intermediate powers",

abstract = "Let G(k) denote the least number s such that every suffciently large natural number is the sum of at most s positive integral kth powers. We show that G(7) ≤ 31, G(8) ≤ 39, G(9) ≤ 47, G(10) ≤ 55, G(11) ≤ 63, G(12) ≤ 72, G(13) ≤ 81, G(14) ≤ 90, G(15) ≤ 99, G(16) ≤ 108.",

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T1 - On Waring's problem for intermediate powers

AU - Wooley, Trevor D

PY - 2016/11/4

Y1 - 2016/11/4

N2 - Let G(k) denote the least number s such that every suffciently large natural number is the sum of at most s positive integral kth powers. We show that G(7) ≤ 31, G(8) ≤ 39, G(9) ≤ 47, G(10) ≤ 55, G(11) ≤ 63, G(12) ≤ 72, G(13) ≤ 81, G(14) ≤ 90, G(15) ≤ 99, G(16) ≤ 108.

AB - Let G(k) denote the least number s such that every suffciently large natural number is the sum of at most s positive integral kth powers. We show that G(7) ≤ 31, G(8) ≤ 39, G(9) ≤ 47, G(10) ≤ 55, G(11) ≤ 63, G(12) ≤ 72, G(13) ≤ 81, G(14) ≤ 90, G(15) ≤ 99, G(16) ≤ 108.

UR - http://arxiv.org/abs/1602.03221

U2 - 10.4064/aa8439-8-2016

DO - 10.4064/aa8439-8-2016

M3 - Article (Academic Journal)

SN - 0065-1036

VL - 176

SP - 241

EP - 247

JO - Acta Arithmetica

JF - Acta Arithmetica

IS - 3

ER -

On Waring's problem for intermediate powers

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