On Bounded Remainder Sets and Strongly Non-Bounded Remainder Sets for Sequences $(\{a_nα\})_{n\geq 1}$

Lisa Kaltenböck; Gerhard Larcher

paper

On Bounded Remainder Sets and Strongly Non-Bounded Remainder Sets for Sequences $({a_{n} α})_{n \geq 1}$

arXiv:1806.10336

Abstract

We give some results on the existence of bounded remainder sets (BRS) for sequences of the form $({a_{n} α})_{n \geq 1}$ , where $(a_{n})_{n \geq 1}$ - in most cases - is a given sequence of distinct integers. Further we introduce the concept of strongly non-bounded remainder sets (S-NBRS) and we show for a very general class of polynomial-type sequences that these sequences cannot have any S-NBRS, whereas for the sequence $({2^{n} α})_{n \geq 1}$ every interval is an S-NBRS.

22 pages, 1 figure

On Bounded Remainder Sets and Strongly Non-Bounded Remainder Sets for Sequences ({an​α})n≥1​

Abstract

On Bounded Remainder Sets and Strongly Non-Bounded Remainder Sets for Sequences $({a_{n} α})_{n \geq 1}$