论文标题
在较高尺寸的Adelic Tori上旋转的剩余剩余集合
Bounded remainder sets for rotations on higher dimensional adelic tori
论文作者
论文摘要
在本文中，我们为所有可能的卷的剩余剩余集合提供了一个简单，明确的结构，对于$ d $ d $ d $ dimensional Adelic torus $ \ mathbb {a}^d/\ mathbb {q}^d $的任何非理性旋转。我们的构建涉及动态系统和对Adele的谐波分析的想法，以及将存在论点降低到圆环$ \ mathbb {r}^d/\ mathbb {q}^d $的几何论点。
In this paper we give a simple, explicit construction of polytopal bounded remainder sets of all possible volumes, for any irrational rotation on the $d$ dimensional adelic torus $\mathbb{A}^d/\mathbb{Q}^d$. Our construction involves ideas from dynamical systems and harmonic analysis on the adeles, as well as a geometric argument that reduces the existence argument to the case of an irrational rotation on the torus $\mathbb{R}^d/\mathbb{Q}^d$.
