Counting β-expansions and the absolute continuity of Bernoulli convolutions

T.M.W. Kempton

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We study the typical growth rate of the number of words of length n which can be extended to β-expansions of x. In the general case we give a lower bound for the growth rate, while in the case that the Bernoulli convolution associated to parameter β is absolutely continuous we are able to give the growth rate precisely. This gives new necessary and sufficient conditions for the absolute continuity of Bernoulli convolutions.
Original languageEnglish
Pages (from-to)189-203
Number of pages15
JournalMonatshefte fur Mathematik
Volume171
DOIs
Publication statusPublished - 2013

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