The asymptotic formula in Waring's problem: Higher order expansions

Robert C. Vaughan; Trevor D Wooley

doi:10.1515/crelle-2015-0098

The asymptotic formula in Waring's problem: Higher order expansions

Robert C. Vaughan, Trevor D Wooley

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Abstract

When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.

Original language	English
Pages (from-to)	17-46
Number of pages	30
Journal	Journal für die reine und angewandte Mathematik
Volume	2018
Issue number	742
Early online date	16 Feb 2016
DOIs	https://doi.org/10.1515/crelle-2015-0098
Publication status	Published - Sept 2018

Keywords

math.NT
11P05
11P55

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title = "The asymptotic formula in Waring's problem: Higher order expansions",

abstract = "When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.",

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T2 - Higher order expansions

AU - Vaughan, Robert C.

AU - Wooley, Trevor D

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N2 - When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.

AB - When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.

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KW - 11P55

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U2 - 10.1515/crelle-2015-0098

DO - 10.1515/crelle-2015-0098

M3 - Article (Academic Journal)

SN - 0075-4102

VL - 2018

SP - 17

EP - 46

JO - Journal für die reine und angewandte Mathematik

JF - Journal für die reine und angewandte Mathematik

IS - 742

ER -

The asymptotic formula in Waring's problem: Higher order expansions

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