Bounded remainder sets for rotations on the adelic torus

2018/03/28 by Furno, Joanna, Haynes, Alan, Koivusalo, Henna
#11J61 #11K38 #37A45 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1803.10559

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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