Geodesic
Quadratic irrationality exponents of certain numbers
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2013), pp. 25-29 
A. A. Polyanskii. Quadratic irrationality exponents of certain numbers. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2013), pp. 25-29. http://geodesic.mathdoc.fr/item/VMUMM_2013_5_a3/
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     author = {A. A. Polyanskii},
     title = {Quadratic irrationality exponents of certain numbers},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2013_5_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper presents upper estimates for the non-quadraticity measure of the numbers $\sqrt{2k+1}\ln\bigr((k+1-\sqrt{2k+1})/k\bigl)$ and $\sqrt{2k-1}\operatorname{arctg}\bigr(\sqrt{2k-1}/(k-1)\bigl)$, where $k\in\mathbb{N}$. In particular, we improved an upper estimate for the non-quadraticity measure of $\ln2$.

[1] Hata M., “$\mathbb{C}^2$-saddle method and Beukers` integral”, Trans. Amer. Math. Soc., 352:10 (2000), 4557–4583 | DOI | MR

[2] Marcovecchio R., “The Rhin–Viola method for $\log 2$”, Acta Arithm., 139:2 (2009), 147–184 | DOI | MR

[3] Polyanskii A.A., “O kvadratichnom pokazatele irratsionalnosti $\ln 2$”, Vestn. Mosk. un-ta. Matem. Mekhan., 2012, no. 1, 25–30 | MR

[4] Nesterenko Yu.V., “O pokazatele irratsionalnosti chisla $\ln2$”, Matem. zametki, 88:4 (2010), 549–564 | DOI

[5] Bashmakova M.G., “Estimates for the exponent of irrationality for certain numbers”, Moscow J. Comb. and Number Theory, 1:1 (2011), 67–78 | MR

[6] Polyanskii A., “On the irrationality measure of certain numbers”, Moscow J. Comb. and Number Theory, 1:4 (2011), 80–90 | MR