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Additive Diophantine inequalities with mixed powers I

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

In this paper we shall be concerned with the following problem. Let k1 ≤ k2 ≤…≤ ks be natural numbers, λ1,…, λs be nonzero real numbers, not all of the same sign. Is it then true that the values taken by

at integer points (x1,…, xs) ∈ ℤk are dense on the real line, provided at least one of the ratios λi/λj, is irrational? We shall refer to this, for brevity, as the inequality problem for k1,…, ks. Optimistically one may conjecture that the inequality problem is true whenever

Type
Research Article
Information
Mathematika , Volume 34 , Issue 2 , December 1987 , pp. 124 - 130
Copyright
Copyright © University College London 1987

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References

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