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Approximants de Padé simultanés de logarithmes. (Simultaneous Padé approximants of logarithms). (French) Zbl 0596.10033
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, \(H=\max (| b|, | c|)\).
Reviewer: F.Beukers

MSC:
11J81 Transcendence (general theory)
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