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A problem in additive number theory

Published online by Cambridge University Press:  24 October 2008

Jörg Brüdern
Jörg Brüdern
Affiliation:
Geismar Landstrasse 97, 3400 Göttingen, West Germany
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Extract

The determination of the minimal s such that all large natural numbers n admit a representation as

is an interesting problem in the additive theory of numbers and has a considerable literature, For historical comments the reader is referred to the author's paper [2] where the best currently known result is proved. The purpose here is a further improvement.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 1 , January 1988 , pp. 27 - 33
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Brüdern, J.. Sums of squares and higher powers. J. London Math. Soc. (2) 35 (1987), 233–243.CrossRefGoogle Scholar
[2]Brüdern, J.. Sums of squares and higher powers. II. J. London Math. Soc. (2) 35 (1987), 244–250.CrossRefGoogle Scholar
[3]Hardy, G. H. and Wright, E. M.. An Introduction to the Theory of Numbers, 5th edn. (Oxford University Press, 1979).Google Scholar
[4]Thanigasalam, K.. On sums of powers and a related problem. Acta Arith. 36 (1980), 125–141.CrossRefGoogle Scholar
[5]Vaughan, R. C.. The Hardy–Littlewood Method (Cambridge University Press, 1981).Google Scholar
[6]Vaughan, R. C.. Some remarks on Weyl sums. In Topics in Classical Number Theory, Colloq. Math. Soc. Janos Bolyai 34 (Elsevier North-Holland, 1984), 1585–1602.Google Scholar
[7]Vaughan, R. C.. On Waring's problem for smaller exponents. Proc. London Math. Soc. (3) 52 (1986), 445–465.CrossRefGoogle Scholar