Abstract
Expansion of real numbers is a basic research topic in number theory. Usually we expand real numbers in one given base. In this paper, we begin to systematically study expansions in multiple given bases in a reasonable way, which is a generalization in the sense that if all the bases are taken to be the same, we return to the classical expansions in one base. In particular, we focus on greedy, quasi-greedy, lazy, quasi-lazy and unique expansions in multiple bases.
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The author thanks Professor Jean-Paul Allouche for his advices and pointing to the paper [29].
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The author is grateful to the Oversea Study Program of Guangzhou Elite Project (GEP) for financial support (JY201815).
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Li, YQ. Expansions in multiple bases. Acta Math. Hungar. 163, 576–600 (2021). https://doi.org/10.1007/s10474-020-01094-7
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DOI: https://doi.org/10.1007/s10474-020-01094-7