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arXiv · 2002.04444

Bounded remainder sets for rotations on higher dimensional adelic tori

Akshat Das·Joanna Furno·Alan Haynes
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Abstract

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 $\mathbb{R}^d/\mathbb{Q}^d$.

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Akshat Das, Joanna Furno, Alan Haynes. 2020-02-10. Bounded remainder sets for rotations on higher dimensional adelic tori. https://doi.org/10.2140/moscow.2021.10.111

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