Geodesic
Irrationality Measures for Continued Fractions With Arithmetic Functions
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 139

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Let $f(n)$ or the base-$2$ logarithm of $f(n)$ be either $d(n)$ (the divisor function), $\sigma(n)$ (the divisor-sum function), $\varphi(n)$ (the Euler totient function), $\omega(n)$ (the number of distinct prime factors of $n$) or $\Omega(n)$ (the total number of prime factors of $n$). We present good lower bounds for $\bigl|\frac MN-\alpha\bigr|$ in terms of $N$, where $\alpha=[0;f(1),f(2),\ldots]$.
DOI : 10.2298/PIM140618001H
Classification : 11J82, 11J70
Keywords: continued fraction, arithmetic functions, measure of irrationality 
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     author = {Jaroslav Han\v{c}l and Kalle Lepp\"al\"a},
     title = {Irrationality {Measures} for {Continued} {Fractions} {With} {Arithmetic} {Functions}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {139 },
     publisher = {mathdoc},
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     year = {2015},
     doi = {10.2298/PIM140618001H},
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Jaroslav Hančl; Kalle Leppälä. Irrationality Measures for Continued Fractions With Arithmetic Functions. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 139 . doi: 10.2298/PIM140618001H

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