Counting -expansions and the absolute continuity of Bernoulli convolutions

We study the typical growth rate of the number of words of length which can be extended to -expansions of . In the general case we give a lower bound for the growth rate, while in the case that the Bernoulli convolution associated to parameter is absolutely continuous we are able to give the growth...

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Bibliographic Details
Published inMonatshefte für Mathematik Vol. 171; no. 2; pp. 189 - 203
Main Author Kempton, Tom
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.08.2013
Subjects
Mathematics
Mathematics and Statistics
28D05
Bernoulli convolutions
Beta expansions
42A85
11A63
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Summary:We study the typical growth rate of the number of words of length which can be extended to -expansions of . In the general case we give a lower bound for the growth rate, while in the case that the Bernoulli convolution associated to parameter 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.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-013-0512-3