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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
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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

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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