Geodesic
An explicit lower bound for a~homogeneous rational linear form in the logarithms of algebraic numbers.~II
Izvestiya. Mathematics , Tome 64 (2000) no. 6, pp. 1217-1269.

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In this paper we establish an estimate for the modulus of a linear form of the type described in the title. This estimate is exponential with respect to the number of summands. 
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E. M. Matveev. An explicit lower bound for a~homogeneous rational linear form in the logarithms of algebraic numbers.~II. Izvestiya. Mathematics , Tome 64 (2000) no. 6, pp. 1217-1269. http://geodesic.mathdoc.fr/item/IM2_2000_64_6_a4/

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