论文标题
一种线性形式的dirichlet频谱
Dirichlet spectrum for one linear form
论文作者
论文摘要
对于$ n \ geq 2 $，我们在线性形式和最大规范中以整个间隔$ [0,1] $来确定$ \ rn $中的Dirichlet Spectrum。这种自然的结果改善了贝雷斯内维奇，关，马纳特，拉米雷斯和维拉尼的最新作品，并补充了作者随后的论文，在该论文中，证明了类似结果的同时近似。可以通过与后一篇论文相似的方法获得的各种概括。我们认为，我们的结果是解决一般形式系统的非常开放的类似问题的重要一步。
For $n\geq 2$, we determine the Dirichlet spectrum in $\Rn$ with respect to a linear form and the maximum norm as the entire interval $[0,1]$. This natural result improves on recent work of Beresnevich, Guan, Marnat, Ramírez and Velani, and complements a subsequent paper by the author where the analogous result was proved for simultaneous approximation. Various generalisations that can be obtained by similar methods as in the latter paper are indicated. We believe that our results are an important step towards resolving the very open analogous problem for a general system of linear forms.
