Schmidt's subspace theorem with moving targets
Schmidt's subspace theorem with moving targets
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DOI：
10.1007/s002220050114
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发表时间：
1997
影响因子：
3.1
通讯作者：
M. Ru;Paul Vojta
中科院分区：
文献类型：
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作者：
M. Ru;Paul Vojta
近年来，由于Vojta、Lang、Osgood等人的工作，人们开始意识到Nevanlinna理论与丢芬图斯近似之间有着密切的关系。P. Vojta编写了一本字典（参见Vojta [V1]），为这两种理论的基本概念提供了对应关系。亚纯函数的第二个主要定理是内万林纳理论中最重要的结果，根据沃伊塔的字典，它在数论中的对应是罗斯定理。1929年，r . Nevanlinna推测，如果P1 (C)中的不同点被不同的全纯映射ai: C→P1 (C)替换为Tai (r)= o (Tf (r))，则第二个主要定理仍然正确，其中Tf (r)是全纯映射f: C→P1 (C)的evanlinna特征函数（定义见[RS 1]）。经过许多人的多次尝试，奥斯古德在1985年证明了这个猜想，这就是现在被称为“动目标第二主定理”的猜想。1986年，Steinmetz给出了另一个简单而优雅的证明。最近，Vojta （[v2]和[v3]）在数论中表述并证明了它的对立物：
In recent years, due to work of Vojta, Lang, Osgood, etc., people have started to realize that there is a close relationship between Nevanlinna theory and Diophantine approximation. P. Vojta has compiled a dictionary (see Vojta [V1]) providing correspondences for the concepts fundamental to the two theories. The second main theorem for meromorphic functions is the most important result in Nevanlinna theory, and its counterpart in number theory, via Vojta’s dictionary, is Roth’s theorem. In 1929, R. Nevanlinna conjectured that the second main theorem remains correct if distinct points in P1 (C) are replaced by distinct holomorphic maps ai: C→ P1 (C) with Tai (r)= o (Tf (r)), where Tf (r) is theNevanlinna characteristic function of the holomorphic map f: C→ P1 (C)(see [RS 1] for the definition). After many attempts by various people, Osgood proved the conjecture in 1985, which is now known as the Second Main Theorem with Moving Targets. In 1986, Steinmetz gave another simple and elegant proof. Recently, Vojta ([V 2] and [V 3]) formulated and proved its counterpart in number theory: