Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T15:06:26.745Z Has data issue: false hasContentIssue false
  • English
  • Français

The simultaneous diophantine approximation of certain kth roots*

Published online by Cambridge University Press:  24 October 2008

Charles F. Osgood
Charles F. Osgood
Affiliation:
University of Illinois, Urbana, Illinois
Get access Rights & Permissions [Opens in a new window]

Extract

In a recent paper in this journal(1) Baker obtained a result giving effectively computable bounds on the simultaneous approximation of certain numbers of the form (ab-1)nj/n by rational numbers of the formpιq-1 where a, b, n, the nι and q are positive integers while the pι are non-negative integers. In this paper we shall obtain explicit bounds on the simultaneous approximation of certain numbers of the form rβ1, …, rβn where β and each rι, 1 ≤ j ≤ n, are positive rational numbers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 1 , January 1970 , pp. 75 - 86
Copyright
Copyright © Cambridge Philosophical Society 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Baker, A.Simultaneous rational approximations to certain algebraic numbers, Proc. Cambridge Philos. Soc.. 63 (1967), 693–702.CrossRefGoogle Scholar
(2)Fel'dman, N. I.Estimation of the absolute value of a linear form from logarithms of certain algebraic numbers. Mat. Zametki, (2) (1967), 245–256.Google Scholar
(3)Rosseb, B.Explicit bounds for some function of prime numbers. Amer. J. Math. 63 (1941), 212–232.Google Scholar