Vol. 10, No. 2, 2021

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Bounded remainder sets for rotations on higher-dimensional adelic tori

Akshat Das, Joanna Furno and Alan Haynes

Vol. 10 (2021), No. 2, 111–120
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 𝔸dd . 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 dd .

Additional material
Keywords
bounded remainder sets, Birkhoff sums, adeles
Mathematical Subject Classification
Primary: 11J61, 11K38, 37A44
Milestones
Received: 25 September 2020
Accepted: 8 January 2021
Published: 23 June 2021
Authors
Akshat Das
Department of Mathematics
University of Houston
Houston, TX
United States
Joanna Furno
Mathematical Sciences
DePaul University
Chicago, IL
United States
Alan Haynes
Department of Mathematics
University of Houston
Houston, TX
United States