论文标题
$ s $ numbers的dirichlet可改善性
Dirichlet improvability for $S$-numbers
论文作者
论文摘要
我们研究了在$ s $ adiC设置中改善Dirichlet定理的公制二芬太汀定理的问题。我们的方法是基于与Dirichlet Ristrability转化为动态性问题的问题的转换，我们证明的主要技术是由于D. Y. Kleinbock和G. Tomanov引起的定量非散布估算的$ S $ - adic版本。本文的主要结果可以被视为D. Y. Kleinbock和B. Weiss的早期作品的数字字段版本，以及第二名的作者和Anish Ghosh的数字版本。这反过来又概括了Shreyasi datta和M. M. Radhika的结果，这是对矢量奇异性的任何数字字段$ k $和包含所有Archimedian地方的$ s $的结果。
We study the problem of improving Dirichlet's theorem of metric Diophantine approximation in the $S$-adic setting. Our approach is based on translation of the problem related to Dirichlet improvability into a dynamical one, and the main technique of our proof is the $S$-adic version of quantitative nondivergence estimate due to D. Y. Kleinbock and G. Tomanov. The main result of this paper can be regarded as the number field version of earlier works of D. Y. Kleinbock and B. Weiss, and of the second named author and Anish Ghosh. Also this in turn generalises a result of Shreyasi Datta and M. M. Radhika on singularity of vectors to any number field $K$ and $S$ containing all archimedian places.
