Abstract
Let f, g be completely multiplicative functions, \({|f(n)| = |g(n)| = 1, (n \in \mathbb{N})}\) such that \({|f ([\sqrt{2n}]) - Cg(n)| \leqq \varepsilon(n),\,\varepsilon(n) \downarrow 0}\) and
We prove that \({f(n) = g(n) = n^{i\tau} , C = (\sqrt{2})^{i\tau}}\).
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References
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Dedicated to the memory of Professor Ferenc Gécseg
Dedicated to the memory of Professor Ferenc Gécseg
This work was completed with the support of the Hungarian and Vietnamese TET (grant agreement no. TET 10-1-2011-0645).
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Kátai, I., Phong, B.M. On the multiplicative group generated by \(\left\{\frac{[\sqrt{2n}]}{n} |\,n \in \mathbb{N}\right\}. {\rm III}\) . Acta Math. Hungar. 147, 247–254 (2015). https://doi.org/10.1007/s10474-015-0518-5
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DOI: https://doi.org/10.1007/s10474-015-0518-5