Exceptional digit frequencies and expansions in non-integer bases

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

Abstract

In this paper we study the set of digit frequencies that are realised by elements of the set of β -expansions. The main result of this paper demonstrates that as β approaches 1, the set of digit frequencies that occur amongst the set of β -expansions fills out the simplex. As an application of our main result, we obtain upper bounds for the local dimension of certain biased Bernoulli convolutions.

Details

Original languageEnglish
Pages (from-to)1–31
JournalMonatshefte fur Mathematik
Volume190
Issue number1
Early online date13 Jun 2019
Publication statusPublished - 1 Sep 2019

Keywords

  • Expansions in non-integer bases, Digit frequencies, Bernoulli convolutions