论文标题
圆形和球上的内在双苯胺近似
Intrinsic Diophantine approximation on circles and spheres
论文作者
论文摘要
我们研究圆圈和球体内在的双磷酸近似产生的拉格朗日光谱。更准确地说，我们考虑嵌入在$ \ mathbb {r}^2 $或$ \ mathbb {r}^3 $中的三个圆圈和嵌入在$ \ mathbb {r}^3 $或$ \ Mathbb {r Mathbb {r}^4 $中的三个球体中。我们提出了一个统一的框架，将这六个空间的拉格朗日光谱与$ \ mathbb {r} $和$ \ mathbb {c} $的光谱连接起来。多亏了Asmus L. schmidt的先前工作，在$ \ Mathbb {r} $和$ \ Mathbb {C} $的光谱上，我们可以作为推论，对于六个光谱中的每个光谱，最小的堆积点和最初的离散部分都完全呈现出来。
We study Lagrange spectra arising from intrinsic Diophantine approximation of circles and spheres. More precisely, we consider three circles embedded in $\mathbb{R}^2$ or $\mathbb{R}^3$ and three spheres embedded in $\mathbb{R}^3$ or $\mathbb{R}^4$. We present a unified framework to connect the Lagrange spectra of these six spaces with the spectra of $\mathbb{R}$ and $\mathbb{C}$. Thanks to prior work of Asmus L.~Schmidt on the spectra of $\mathbb{R}$ and $\mathbb{C}$, we obtain as a corollary, for each of the six spectra, the smallest accumulation point and the initial discrete part leading up to it completely.
