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Linear Forms in two m-adic Logarithms and Applications to Diophantine Problems

Published online by Cambridge University Press:  04 December 2007

Yann Bugeaud
Yann Bugeaud
Affiliation:
Université Louis Pasteur, UFR de mathématiques, 7, rue René Descartes, 67084 Strasbourg, France. E-mail: bugeaud@math.u-strasbg.fr
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Abstract

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We give sharp, explicit estimates for linear forms in two logarithms, simultaneously for several non-Archimedean valuations. We present applications to explicit lower bounds for the fractional part of powers of rational numbers, and to the Diophantine equation (xn − 1)/(x − 1) = yq.

Keywords

Baker's methodDiophantine equationLinear form in logarithmsnon-Archimedean approximation
Type
Research Article
Information
Compositio Mathematica , Volume 132 , Issue 2 , June 2002 , pp. 137 - 158
Copyright
© 2002 Kluwer Academic Publishers