Diophantine approximation for products of linear maps - logarithmic improvements
Diophantine approximation for products of linear maps - logarithmic improvements
复制标题
线性映射乘积的丢番图近似 - 对数改进
DOI：
10.1090/tran/6953
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发表时间：
2017
影响因子：
1.3
通讯作者：
Gorodnik A
中科院分区：
文献类型：
--
作者：
Gorodnik A
本文研究了乘性丢番图逼近中的一个Cassels问题，该问题涉及仿射线性形式乘积在积分点处的极小值问题。我们以前知道，这个乘积的值可以任意接近于零，我们确定，事实上，它们以显式速率近似于零。我们的方法是基于调查数量密度的轨道的高阶阿贝尔群。引用
This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed at integral points. It was previously known that values of this product become arbitrary close to zero, and we establish that, in fact, they approximate zero with an explicit rate. Our approach is based on investigating quantitative density of orbits of higher-rank abelian groups. References