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

  • Robert C. Vaughan EMAIL logo and Trevor D. Wooley

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.

Funding statement: The first author was supported in part by NSA grant no. H98230-12-1-0276.

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Received: 2013-08-30
Revised: 2015-10-27
Published Online: 2016-02-16
Published in Print: 2018-09-01

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