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Additive Diophantine inequalities with mixed powers II

Published online by Cambridge University Press:  26 February 2010

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

A classical problem in the additive theory of numbers is the determination of the minimal s such that for all sufficiently large n the equation

is solvable in natural numbers xk. Improving on earlier results the author [2] has been able to prove that one may take s = 18. In a survey article W. Schwarz asked for an analogue for diophantine inequalities [6]. As a first contribution to this subject we prove

Theorem. Let λ2, …, λ23 be nonzero real numbers, λ2/λ3 irrational. Then the values taken by

at integer points ( x1, …, x22) are dense on the real line.

Type
Research Article
Information
Mathematika , Volume 34 , Issue 2 , December 1987 , pp. 131 - 140
Copyright
Copyright © University College London 1987

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References

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