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On Waring’s problem: Three cubes and a minicube

Published online by Cambridge University Press:  11 January 2016

Jörg Brüdern  and
Trevor D. Wooley
Jörg Brüdern
Affiliation:
Mathematisches Institut, D-37073 Göttingen, Germany, [email protected]
Trevor D. Wooley
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom, [email protected]
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Abstract

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We establish that almost all natural numbers n are the sum of four cubes of positive integers, one of which is no larger than n5/36. The proof makes use of an estimate for a certain eighth moment of cubic exponential sums, restricted to minor arcs only, of independent interest.

Keywords

11P0511P55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 200 , December 2010 , pp. 59 - 91
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

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