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

Part of: Diophantine approximation, transcendental number theory Diophantine equations

Published online by Cambridge University Press:  07 February 2013

CLAUDE LEVESQUE  and
MICHEL WALDSCHMIDT
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
*
✉Claude.Levesque@mat.ulaval.ca
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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.

Keywords

Diophantine equationsDiophantine approximationLiouville inequalityfamilies of Thue–Mahler equations

MSC classification

Secondary: 11D59: Thue-Mahler equations 11J68: Approximation to algebraic numbers 11J86: Linear forms in logarithms; Baker's method 11J17: Approximation by numbers from a fixed field
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 93 , Issue 1-2 , October 2012 , pp. 121 - 131
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc.

References

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