Approximants de Padé simultanés de logarithmes. (Simultaneous Padé approximants of logarithms) (Q1078236)

By constructing explicit simultaneous Padé approximations the authors manage to give explicit lower bounds for certain linear forms in logarithms. Although the lower bound is extremely good in comparison with Baker's estimates, the range of applicability is very limited. A typical example is: \[ | a+b \log (3/4)+c \log (5/4)| \quad \geq \quad \exp (-(88 \log H+196)), \] where a,b,c\(\in {\mathbb{Z}}\) not all zero, \(H=\max (| b|, | c|)\).