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Linear independence of the real numbers generated by the square and cube subsequences of Thue–Morse
Acta Mathematica Hungarica ( IF 0.9 ) Pub Date : 2024-02-29 , DOI: 10.1007/s10474-024-01417-y E. Miyanohara
更新日期：2024-02-29
Acta Mathematica Hungarica ( IF 0.9 ) Pub Date : 2024-02-29 , DOI: 10.1007/s10474-024-01417-y E. Miyanohara
Let \((t(m))_{m \ge0}\) be Thue-Morse sequence and \(b>2\) be an integer. In this paper, we prove that the real numbers \(1\), \(\sum_{m=0}^\infty {\frac{t(m^2)}{{b}^{m+1}}}\) and \(\sum_{m=0}^\infty {\frac{t(m^3)}{{b}^{m+1}}}\) are linearly independent over \(\mathbb{Q}\).
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