Some metrical theorems in diophantine approximation
v. on a conjecture of mahler
Published online by Cambridge University Press: 24 October 2008
Extract
Introduction. If ξ is a real number we denote by ∥ ξ ∥ the difference between ξ and the nearest integer, i.e.
It is well known (e.g. Koksma (3), I, Satz 4) that if θ1, θ2, …, θn are any real numbers, the inequality
has infinitely many integer solutions q > 0. In particular, if α is any real number, the inequality
has infinitely many solutions.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 1 , January 1951 , pp. 18 - 21
- Copyright
- Copyright © Cambridge Philosophical Society 1951
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