A Groshev type theorem for convergence on manifolds

V. Beresnevich

doi:10.1023/A:1015662722298

A Groshev type theorem for convergence on manifolds

V. Beresnevich

Mathematics

Research output: Contribution to journal › Article › peer-review

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

Original language	English
Pages (from-to)	99-130
Journal	Acta Mathematica Hungarica
Volume	94
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1015662722298
Publication status	Published - 2002

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10.1023/A:1015662722298

http://link.springer.com/article/10.1023%2FA%3A1015662722298

Cite this

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AB - 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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