Geodesic
Approximating $\ln 2$ by numbers in the field $\mathbb{Q}(\sqrt{2}\,)$
Izvestiya. Mathematics , Tome 82 (2018) no. 3, pp. 549-577

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Using a new integral construction combining the idea of symmetry suggested by the second author in 2007 and the integral introduced by Marcovecchio in 2009, we obtain a new bound for the approximation of $\ln{2}$ by numbers in the field $\mathbb{Q}(\sqrt{2}\,)$.
Keywords: irrationality measure, linear form, complex integral. 
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     author = {M. Yu. Luchin and V. Kh. Salikhov},
     title = {Approximating $\ln 2$ by numbers in the field $\mathbb{Q}(\sqrt{2}\,)$},
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M. Yu. Luchin; V. Kh. Salikhov. Approximating $\ln 2$ by numbers in the field $\mathbb{Q}(\sqrt{2}\,)$. Izvestiya. Mathematics , Tome 82 (2018) no. 3, pp. 549-577. http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a5/