论文标题
定量的Khintchine-Groshev定理用于S-砷二苯胺近似
A quantitative Khintchine-Groshev theorem for S-arithmetic Diophantine approximation
论文作者
论文摘要
施密特（Schmidt）在1960年的论文中研究了一种定量类型的Khintchine-Groshev定理，以实现一般（更高）维度。最近，找到了定理的新证明，这使得放宽维度约束是可能的，更普遍地增加了M. Alam，A。Ghosh和S. Yu的一致性条件。 在本文中，我们将这种新方法概括为S-砷空间，并获得s-砷的khintchine-groshev定理的定量版本。实际上，我们考虑了一种新的S-arthmetic类似物近似值，该类似物与以前建立的近似不同（参见2007年的D. Kleinbock和G. Tomanov的论文）。因此，为了完整，我们还基于这种新的概括来处理Khintchine-Groshev定理的收敛案例。
In his 1960 paper, Schmidt studied a quantitative type of Khintchine-Groshev theorem for general (higher) dimensions. Recently, a new proof of the theorem was found, which made it possible to relax the dimensional constraint and more generally, to add on the congruence condition by M. Alam, A. Ghosh, and S. Yu. In this paper, we generalize this new approach to S-arithmetic spaces and obtain a quantitative version of an S-arithmetic Khintchine-Groshev theorem. In fact, we consider a new S-arithmetic analog of Diophantine approximation, which is different from the one formerly established (see the 2007 paper of D. Kleinbock and G. Tomanov). Hence for the sake of completeness, we also deal with the convergence case of the Khintchine-Groshev theorem, based on this new generalization.
