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Cubic Diophantine inequalities

Published online by Cambridge University Press:  26 February 2010

R. C. Baker
R. C. Baker
Affiliation:
Royal Holloway College, Egham, Surrey.
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Let λ1, …, λ8 be any non-zero real numbers not all of the same sign and not all in rational ratios. According to a theorem of Davenport and Roth [3], given a real number κ, the inequality

has infinitely many solutions in positive integers for any ε > 0. Recently Liu, Ng and Tsang [5] gave a refinement of this result: for any δ > 0, the inequality

has infinitely many solutions in positive integers. In the present note we obtain a better exponent.

Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 83 - 92
Copyright
Copyright © University College London 1982

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References

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