No CrossRef data available.
Article contents
Cubic Diophantine inequalities
Published online by Cambridge University Press: 26 February 2010
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.
Information
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 1988
References
1.Baker, R. C.. Cubic diophantine inequalities. Mathematika, 29 (1982), 83–92.CrossRefGoogle Scholar
2.Baker, R. C. and Harman, G.. Diophantine inequalities with mixed powers. J. Number Theory, 18 (1984), 69–85.CrossRefGoogle Scholar
3.Brüdern, J.. Addtive diophantine inequalities with mixed powers I. Mathematika, 34 (1987), 124–130.CrossRefGoogle Scholar
4.Brüdern, J.. Addtive diophantine inequalities with mixed powers II. Mathematika, 34 (1987), 131–142.CrossRefGoogle Scholar
6.Davenport, H.. On indefinite quadratic forms in many variables. Mathematika, 3 (1956), 81–101.CrossRefGoogle Scholar
7.Davenport, H. and Roth, K. F.. The solubility of certain diophantine inequalities. Mathematika, 2 (1955), 81–96.CrossRefGoogle Scholar
8.Liu, M. C., Ng, S.-M. and Tsang, K. M.. An improved estimate for certain diophantine inequalities. Proc. Amer. Math. Soc., 78 (1980), 457–463.CrossRefGoogle Scholar
10.Vaughan, R. C.. Sums of three cubes. Bull. London Math. Soc., 17 (1985), 17–20.CrossRefGoogle Scholar
11.Vaughan, R. C.. On Waring's problem for cubes. J. reine angew. Math., 365 (1986), 122–170.Google Scholar
- 6
- Cited by