Intrinsic Diophantine approximation on circles and spheres

IF 0.8 3区数学 Q2 MATHEMATICS Mathematika Pub Date : 2023-10-26 DOI:10.1112/mtk.12228

Byungchul Cha, Dong Han Kim

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引用次数: 0

Abstract

We study Lagrange spectra arising from intrinsic Diophantine approximation of circles and spheres. More precisely, we consider three circles embedded in $R^{2}$ or $R^{3}$ and three spheres embedded in $R^{3}$ or $R^{4}$ . We present a unified framework to connect the Lagrange spectra of these six spaces with the spectra of $R$ and $C$ . Thanks to prior work of Asmus L. Schmidt on the spectra of $R$ and $C$ , 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.

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圆和球面的内禀丢番图近似

我们研究了由圆和球体的固有丢番图近似引起的拉格朗日谱。更确切地说，我们考虑嵌入R2$\mathbb｛R｝^2$或R3$\mathbb{R｝^3$中的三个圆和嵌入R3中的三个子球$\mathbb｛R｝^3$或R 4$\mathbb{R｝^ 4$。我们提出了一个统一的框架来连接这六个空间的拉格朗日谱与R$\mathbb{R}$和C$\mathbb{C}$的谱。由于Asmus L.Schmidt先前对R$\mathbb｛R｝$和C$\mathbb｛C｝$的谱所做的工作，我们得到了六个谱中每一个谱的最小累积点和完全通向它的初始离散部分。

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.

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