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Simultaneous approximation of zero by values of integral polynomials with respect to different valuations. (English) Zbl 1108.11050

Summary: We prove an analogue of the convergence part of Khintchine’s theorem for the simultaneous approximation of zero in \(\mathbb R\times \mathbb C\times \mathbb Q_p\) by the values of polynomials \(P_n(y)\in \mathbb Z[y]\). This is a proof of a stronger version of V. Sprindzhuk’s conjecture (1980).

MSC:

11J61 Approximation in non-Archimedean valuations
11J83 Metric theory
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