A Groshev Type Theorem for Convergence on Manifolds
A Groshev Type Theorem for Convergence on Manifolds
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流形收敛的格罗舍夫型定理
DOI：
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发表时间：
2002
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通讯作者：
V. Beresnevich
中科院分区：
文献类型：
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作者：
V. Beresnevich
本文讨论了非退化流形上的丢番图逼近，并证明了类似于Khintchine-Groshev定理的一个结果。我们所考虑的问题首先是由A. Baker [1]的有理正态曲线。非退化流形构成了一个大类，包括任何不包含在超平面中的连通解析流形。我们还提出了一种新的方法，它发展了Sprindzuk的经典方法的基本和非基本域的想法，他首先使用解决马勒的问题[28]。
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 [28].