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Fractional parts of powers of rational numbers

Published online by Cambridge University Press:  24 October 2008

M. Bennett
M. Bennett
Affiliation:
University of British Columbia, British Columbia, Canada, V6T 1Z2
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Abstract

The author uses Padé approximation techniques and an elementary lemma on primes dividing binomial coefficients to sharpen a theorem of F. Beukers on fractional parts of powers of rationals. In particular, it is proven that ‖((N+ l)/N)k‖ > 3–k holds for all positive integers N and k satisfying 4 ≤ N ≤ k · 3k. Other results are described including an effective version of a theorem of K. Mahler for a restricted class of rationals.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 2 , September 1993 , pp. 191 - 201
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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