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Cubic Diophantine inequalities

Published online by Cambridge University Press:  26 February 2010

Jörg Brüdern
Jörg Brüdern
Affiliation:
Geismar Landstrasse 97, 3400 Göttingen, Federal Republic of Germany.
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Extract

It was shown by Davenport and Roth [7] that the values taken by

at integer points ( x1, …, x8) ∈ ℤ8 are dense on the real line, providing at least one of the ratios λi/λj, is irrational. Here and throughout, λi denote such nonzero real numbers. More precisely, Liu, Ng and Tsang [8] showed that for all the inequality

has infinitely many solutions in integers. Later Baker [1] obtained the same result in the enlarged range . In this note we improve this further, the progress being considerable.

Type
Research Article
Information
Mathematika , Volume 35 , Issue 1 , June 1988 , pp. 51 - 58
Copyright
Copyright © University College London 1988

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References

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