This article is cited in 9 papers

On the linear independence of numbers over number fields

E. V. Bedulev

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 511.364

Received: 26.08.1997

DOI: 10.4213/mzm1425

 English version: Mathematical Notes, 1998, 64:4, 440–449

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