Bounded remainder sets for rotations on the adelic torus

Furno, Joanna; Haynes, Alan; Koivusalo, Henna

doi:10.1090/proc/14636

Bounded remainder sets for rotations on the adelic torus
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by Joanna Furno, Alan Haynes and Henna Koivusalo PDF

Proc. Amer. Math. Soc. 147 (2019), 5105-5115 Request permission

Abstract:

In this paper we give an explicit construction of bounded remainder sets of all possible volumes for any irrational rotation on the adelic torus $\mathbb {A}/\mathbb {Q}$. Our construction involves ideas from dynamical systems and harmonic analysis on the adeles, as well as a geometric argument which originated in the study of deformation properties of mathematical quasicrystals.

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