Abstract
We obtain some new results in the theory of linear forms in logarithms on a commutative algebraic group, defined over Q . We generalize recent progress of S. David and N. Hirata [1]. In particular, we achieve an optimal linear independence measure in the height of the linear form and a measure more precise than Hirata's [4] for parameters related to the logarithms. The proof rests on Baker's method and a new argument of arithmetical nature.
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