Linear Forms in two m-adic Logarithms and Applications to Diophantine Problems |
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| Authors: | Yann Bugeaud |
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| Institution: | (1) Université Louis Pasteur, UFR de mathématiques, 7, rue René Descartes, 67084 Strasbourg, France |
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| Abstract: | 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 (x
n
– 1)/(x – 1) = y
q
. |
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| Keywords: | Baker's method Diophantine equation Linear form in logarithms non-Archimedean approximation |
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