Geodesic
On simultaneous approximations of $\ln3$ and $\pi/\sqrt3$ by rational numbers
Sbornik. Mathematics, Tome 210 (2019) no. 4, pp. 589-605
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We prove an upper bound for the exponent of the simultaneous approximation of $\ln3$ and $\pi/\sqrt3$ by rational numbers. Bibliography: 16 titles.
Keywords: irrationality measure, simultaneous approximations. 
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A. A. Polyanskii. On simultaneous approximations of $\ln3$ and $\pi/\sqrt3$ by rational numbers. Sbornik. Mathematics, Tome 210 (2019) no. 4, pp. 589-605. http://geodesic.mathdoc.fr/item/SM_2019_210_4_a5/

[1] L. V. Danilov, “Rational approximations of some functions at rational points”, Math. Notes, 24:4 (1978), 741–746 | DOI | MR | Zbl

[2] V. A. Androsenko, “Irrationality measure of the number $\frac{\pi}{\sqrt{3}}$”, Izv. Math., 79:1 (2015), 1–17 | DOI | DOI | MR | Zbl

[3] G. Rhin, “Approximants de Padé et mesures effectives d'irrationalité”, Séminaire de théorie des nombres, Paris 1985–86, Progr. Math., 71, Birkhäuser Boston, Boston, MA, 1987, 155–164 | DOI | MR | Zbl

[4] Qiang Wu, Lihong Wang, “On the irrationality measure of $\log 3$”, J. Number Theory, 142 (2014), 264–273 | DOI | MR | Zbl

[5] V. Kh. Salikhov, “On the irrationality measure of $ \ln 3$”, Dokl. Math., 76:3 (2007), 955–957 | DOI | MR | Zbl

[6] Yu. V. Nesterenko, “On the irrationality exponent of the number $\ln 2$”, Math. Notes, 88:4 (2010), 530–543 | DOI | DOI | MR | Zbl

[7] M. G. Bashmakova, “Estimates for the exponent of irrationality for certain values of hypergeometric functions”, Mosc. J. Comb. Number Theory, 1:1 (2011), 67–78 | MR | Zbl

[8] A. A. Polyanskii, “Square exponent of irrationality of $\ln 2$”, Moscow Univ. Math. Bull., 67:1 (2012), 23–28 | DOI | MR | Zbl

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

[10] A. A. Polyanskii, “Quadratic irrationality exponents of certain numbers”, Moscow Univ. Math. Bull., 68:5 (2013), 237–240 | DOI | MR | Zbl

[11] A. A. Polyanskii, “On the irrationality measures of certain numbers. II”, Math. Notes, 103:4 (2018), 626–634 | DOI | DOI | MR | Zbl

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

[13] E. T. Whittaker, G. N. Watson, A course of modern analysis. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, 4th ed., Cambridge Univ. Press, Cambridge, 1927, vi+608 pp. | MR | Zbl

[14] A. A. Polyanskii, Kompyuternye vychisleniya, 2017 http://polyanskii.com/wp-content/uploads/number-theory/sim-approximations.nb

[15] A. A. Polyanskii, O pokazatelyakh irratsionalnosti nekotorykh chisel, Diss. ... kand. fiz.-matem. nauk, MGU, mekh.-matem. fak-t, M., 2013, 138 pp. http://polyanskii.com/wp-content/uploads/thesis/polyanskii-phd.pdf

[16] M. Hata, “Rational approximations to $\pi$ and some other numbers”, Acta Arith., 63:4 (1993), 335–349 | DOI | MR | Zbl