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Joint approximations of real and $$p$$-adic numbers by algebraic integers. (Russian. English summary) Zbl 1247.11094
Summary: We consider the problem of joint approximations of two points from the fields $$\mathbb C$$ and $${\mathbb Q}_ p$$, respectively, by two algebraic integers. The distance between these numbers is determined by the absolute and $$p$$-adic metrics. As an auxiliary result, we prove a version of Minkowski’s theorem on consecutive minima taking into account the inequality in the $$p$$-adic metric along with the inequalities in the absolute metric.
##### MSC:
 11J13 Simultaneous homogeneous approximation, linear forms 11J61 Approximation in non-Archimedean valuations