Small points on rational subvarieties of tori (Q424808)

Summary: Let \(V\) be a subvariety of a torus defined over the rational numbers. We study the distribution of points of small Weil's height on \(V\). We simplify the proof and we improve previous results by the first author and \textit{S. David} [J. Reine Angew. Math. 513, 145--179 (1999; Zbl 1011.11045)]. We obtain a totally explicit version of a generalized \textit{E. Dobrowolski} result on the Lehmer problem [Acta Arith. 34, 391--401 (1979; Zbl 0416.12001)].