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APPROXIMATION OF AN ALGEBRAIC NUMBER BY PRODUCTS OF RATIONAL NUMBERS AND UNITS

Published online by Cambridge University Press:  07 February 2013

CLAUDE LEVESQUE*
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec (Québec), Canada G1V 0A6
MICHEL WALDSCHMIDT
Affiliation:
Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, F-75252 Paris Cedex 05, France email miw@math.jussieu.fr
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Abstract

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We relate a previous result of ours on families of Diophantine equations having only trivial solutions with a result on the approximation of an algebraic number by products of rational numbers and units. We compare this approximation with a Liouville type estimate, and with an estimate arising from a lower bound for a linear combination of logarithms.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc.

References

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