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Sums of three cubes

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  26 February 2010

Trevor D. Wooley
Trevor D. Wooley
Affiliation:
Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109-1109, U.S.A. E-mail: wooley@math.lsa.umich.edu
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Extract

The set of integers represented as the sum of three cubes of natural numbers is widely expected to have positive density (see Hooley [7] for a discussion of this topic). Over the past six decades or so, the pursuit of an acceptable approximation to the latter statement has spawned much of the progress achieved in the theory of the Hardy-Littlewood method, so far as its application to Waring's problem for smaller exponents is concerned. Write R(N) for the number of positive integers not exceeding N which are the sum of three cubes of natural numbers.

MSC classification

Secondary: 11P05: Waring's problem and variants

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Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 53 - 61
Copyright
Copyright © University College London 2000

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