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Exceptional digit frequencies and expansions in non-integer bases
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Baker, Simon (2019) Exceptional digit frequencies and expansions in non-integer bases. Monatshefte fur Mathematik, 190 . pp. 1-31. doi:10.1007/s00605-019-01311-8 ISSN 0026-9255.
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Official URL: https://doi.org/10.1007/s00605-019-01311-8
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
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Journal or Publication Title: | Monatshefte fur Mathematik | ||||||||
| Publisher: | Springer Vienna | ||||||||
| ISSN: | 0026-9255 | ||||||||
| Official Date: | September 2019 | ||||||||
| Dates: |
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| Volume: | 190 | ||||||||
| Page Range: | pp. 1-31 | ||||||||
| DOI: | 10.1007/s00605-019-01311-8 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Monatshefte fur Mathematik. The final authenticated version is available online at: http://dx.doi.org/[insert DOI]”. | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 12 June 2019 | ||||||||
| Date of first compliant Open Access: | 3 July 2019 | ||||||||
| Related URLs: | |||||||||
| Open Access Version: |
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