Geodesic
On the Irrationality Exponent of the Number $\ln2$
Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 549-564

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We propose another method of deriving the Marcovecchio estimate for the irrationality measure of the number $\ln2$ following, for the most part, the method of proof of the irrationality of the number $\zeta(3)$ proposed by the author in 1996. The proof uses single complex integrals, the so-called Meyer $G$-functions, and is much simpler than that of Marcovecchio.
Keywords: irrational number, Marcovecchio estimate, irrationality measure, irrationality exponent, Meyer $G$-function, saddle-point method. 
@article{MZM_2010_88_4_a6,
     author = {Yu. V. Nesterenko},
     title = {On the {Irrationality} {Exponent} of the {Number} $\ln2$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {549--564},
     publisher = {mathdoc},
     volume = {88},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a6/}
}
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Yu. V. Nesterenko. On the Irrationality Exponent of the Number $\ln2$. Matematičeskie zametki, Tome 88 (2010) no. 4, pp. 549-564. http://geodesic.mathdoc.fr/item/MZM_2010_88_4_a6/