On Baker type lower bounds for linear forms (Q2804244)

A celebrated method of \textit{A. Baker} [Transcendental number theory. Paperback ed. Cambridge etc.: Cambridge University Press (1990; Zbl 0715.11032)] is based on explicit lower bounds for linear forms in the logarithms of algebraic numbers of the form NEWLINE\[NEWLINE|b_1\log \alpha_1+\ldots+b_m\log \alpha_m| >F(B)NEWLINE\]NEWLINE where \(b_1,\ldots,b_m\) are integers with \(B=\max |b_i|\) and the lower bound depends on \(m\) and the heights of the algebraic numbers \(\alpha_1,\ldots,\alpha_m\).NEWLINENEWLINEThe author of the present paper investigates the reciprocal question. Given \(\theta_1,\ldots,\theta_m\), under what conditions is it possible to explicitly give a lower bound NEWLINE\[NEWLINE |b_1\theta_1+\ldots+b_m \theta_m|>F(B).NEWLINE\]NEWLINE The paper studies the case when \(b_1,\ldots,b_m\) are integers in an imaginary quadratic field.