Exceptional digit frequencies and expansions in non-integer bases

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Colleges, School and Institutes


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.


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


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