Geodesic
On the linear independence of numbers over number fields
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 506-517

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In the present paper, the problem of a lower bound for the measure of linear independence of a given collection of numbers $\theta_1,\dots,\theta_n$ is considered under the assumption that, for a sequence of polynomials whose coefficients are algebraic integers, upper and lower estimates at the point $(\theta_1,\dots,\theta_n)$ are known. We use a method that generalizes the Nesterenko method to the case of an arbitrary algebraic number field. 
@article{MZM_1998_64_4_a2,
     author = {E. V. Bedulev},
     title = {On the linear independence of numbers over number fields},
     journal = {Matemati\v{c}eskie zametki},
     pages = {506--517},
     publisher = {mathdoc},
     volume = {64},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a2/}
}
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E. V. Bedulev. On the linear independence of numbers over number fields. Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 506-517. http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a2/