Common expansions in noninteger bases

Vilmos Komornik, Attila Petho

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3 Citations (Scopus)

Abstract

In this paper we study the existence of simultaneous representations of real numbers in bases p > q > 1 with the digit set A = {-m, ⋯ ; 0, ⋯ m}. We prove among others that if q > (1+√8m + 1)/2, then there is a continuum of sequences (ci) ∈A1 satisfying σt=1 ciq-1 = σt=1 cip-1. On the other hand, if q ≥ m+1+ √m(m + 1), then only the trivial sequence (ci) = 0 satisfies the former equality.

Original languageEnglish
Pages (from-to)489-501
Number of pages13
JournalPublicationes Mathematicae
Volume85
Issue number3-4
DOIs
Publication statusPublished - Jan 1 2014

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Keywords

  • Interval filling sequences
  • Simultaneous Rényi expansion

ASJC Scopus subject areas

  • Mathematics(all)

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