Article contents
Simultaneous Diophantine approximation
Published online by Cambridge University Press: 09 April 2009
Abstract
Using a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394. This improves an earlier result of Davenport, who shows that the same conclusion holds if c > 1/46¼ = 1/2.6043 ….
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 24 , Issue 3 , November 1977 , pp. 266 - 285
- Copyright
- Copyright © Australian Mathematical Society 1977
References
- 5
- Cited by