Linear forms in two m-adic logarithms and applications to Diophantine problems

摘要

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). [References: 32]