Geodesic
An inequality for a linear form in the logarithms of algebraic numbers
Matematičeskie zametki, Tome 5 (1969) no. 6, pp. 681-689 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\ln\alpha_1,\dots,\ln\alpha_{m-1}$ be the logarithms of fixed algebraic numbers which are linearly independent over the field of rational numbers, $b_1,\dots,b_{m-1}$ rational integers, $\delta>0$. A bound from below is deduced for the height of the algebraic number $\alpha_m$ under the condition that $$ |b_1\ln\alpha_1+\dots+b_{m-1}\ln\alpha_{m-1}-\ln\alpha_m|<\exp\{-\delta H\}, \quad H=\max|b_k|>0. $$ 
@article{MZM_1969_5_6_a4,
     author = {N. I. Fel'dman},
     title = {An~inequality for a~linear form in the logarithms of algebraic numbers},
     journal = {Matemati\v{c}eskie zametki},
     pages = {681--689},
     year = {1969},
     volume = {5},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_6_a4/}
}
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N. I. Fel'dman. An inequality for a linear form in the logarithms of algebraic numbers. Matematičeskie zametki, Tome 5 (1969) no. 6, pp. 681-689. http://geodesic.mathdoc.fr/item/MZM_1969_5_6_a4/