2 papers
math.NT2021
A three gap theorem for the adeles
Akshat Das, Alan Haynes
We prove a natural generalization of the classical three gap theorem, for rotations on adelic tori. Our proof is an adaptation to the adeles of the lattice based approach to gaps p…
math.NT2020
Bounded remainder sets for rotations on higher dimensional adelic tori
Akshat Das, Joanna Furno, Alan Haynes
In this paper we give a simple, explicit construction of polytopal bounded remainder sets of all possible volumes, for any irrational rotation on the dimensional adelic torus $…