A Groshev type theorem for convergence on manifolds

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JournalActa Mathematica Hungarica
DatePublished - 2002
Issue number1-2
Volume94
Pages (from-to)99-130
Original languageEnglish

Abstract

We deal with Diophantine approximation on the so-called non-degenerate manifolds and prove an analogue of the Khintchine–Groshev theorem. The problem we consider was first posed by A. Baker [1] for the rational normal curve. The non-degenerate manifolds form a large class including any connected analytic manifold which is not contained in a hyperplane. We also present a new approach which develops the ideas of Sprindzuk"s classical method of essential and inessential domains first used by him to solve Mahler"s problem

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