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Expansions in multiple bases

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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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Acknowledgements

The author thanks Professor Jean-Paul Allouche for his advices and pointing to the paper [29].

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu – Paris Rive Gauche, Sorbonne Université – Campus Pierre et Marie Curie, Paris, 75005, France

    Y.-Q. Li

  2. School of Mathematics, South China University of Technology, Guangzhou, 510641, P.R. China

    Y.-Q. Li

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  1. Y.-Q. Li
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Correspondence to Y.-Q. Li.

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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

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