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

Robert C. Vaughan, Trevor D. Wooley

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)17-46
Number of pages30
JournalJournal fur die Reine und Angewandte Mathematik
Volume2018
Issue number742
DOIs
StatePublished - Sep 1 2018

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Waring's problem
Natural number
Asymptotic Formula
Asymptotic Expansion
Higher Order
Term

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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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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The asymptotic formula in Waring's problem : Higher order expansions. / Vaughan, Robert C.; Wooley, Trevor D.

In: Journal fur die Reine und Angewandte Mathematik, Vol. 2018, No. 742, 01.09.2018, p. 17-46.

Research output: Contribution to journalArticle

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