On well-approximable matrices over a field of formal series
On well-approximable matrices over a field of formal series
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DOI：
10.1017/s0305004103006911
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发表时间：
2003-08
影响因子：
0.8
通讯作者：
S. Kristensen
中科院分区：
文献类型：
--
作者：
S. Kristensen
这是一个著名的结果丢番图逼近实数的元素$x \in {\mathbb{R}}$，使得$\Vert qx \Vert 1$的勒贝格测度。类似的结果是已知的矩阵在实数以及$p$-adics。本文证明了系数来自给定有限域的Laurent级数域上的矩阵的相应的多维结果。
It is a well-known result in Diophantine approximation over the reals that the Lebesgue measure of the elements $x \in {\mathbb{R}}$, such that $\Vert qx \Vert 1$. Similar results are known for matrices over the reals as well as the $p$-adics. In this paper, we prove the corresponding multi-dimensional result for matrices over the field of Laurent series with coefficients from a given finite field.