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Linear independence of series related to the Thue–Morse sequence along powers
Published online by Cambridge University Press: 06 March 2024
Abstract
The Thue–Morse sequence $\{t(n)\}_{n\geqslant 0}$ is the indicator function of the parity of the number of ones in the binary expansion of nonnegative integers n, where $t(n)=1$ (resp. $=0$) if the binary expansion of n has an odd (resp. even) number of ones. In this paper, we generalize a recent result of E. Miyanohara by showing that, for a fixed Pisot or Salem number $\beta>\sqrt {\varphi }=1.272019\ldots $, the set of the numbers
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society
Footnotes
This work was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. This research was partly supported by JSPS KAKENHI Grant Number JP22K03263.