On the linear independence of numbers over number fields

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.