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),..., 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),..., theta(n)) are known. We use a method that generalizes the Nesterenko method to the case of an arbitrary algebraic number field.