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Linear independence of the real numbers generated by the square and cube subsequences of Thue–Morse
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 \(\mathbb{Q}\).
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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