Abstract

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 ${ℝ}^d∕{\mathbb{Q}}^d$.

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