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On Waring's problem for cubes

Published online by Cambridge University Press:  24 October 2008

Jörg Brüdern
Jörg Brüdern
Affiliation:
Mathematisches Institut, Bunsenstrasse 3–5, D-3400 Göttingen, Germany
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Extract

A classical conjecture in the additive theory of numbers is that all sufficiently large natural numbers may be written as the sum of four positive cubes of integers. This is known as the Four Cubes Problem, and since the pioneering work of Hardy and Littlewood one expects a much more precise quantitative form of the conjecture to hold. Let v(n) be the number of representations of n in the proposed manner. Then the expected formula takes the shape

where (n) is the singular series associated with four cubes as familiar in the Hardy–Littlewood theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 2 , March 1991 , pp. 229 - 256
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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