On the number of linear forms in logarithms

preprint2008arXivOpen access

Abstract

Let nn be a positive integer. In this paper we estimate the size of the set of linear forms b1log⁡a1+b2log⁡a2+...+bnlog⁡anb_1\log a_1 + b_2\log a_2+...+b_n\log a_n, where ∣bi∣≤Bi|b_i|\leq B_i and 1≤ai≤Ai1\leq a_i\leq A_i are integers, as Ai,Bi→∞A_i,B_i\to \infty.

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