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On the irrationality measure of \(\ln 7\). (English. Russian original) Zbl 1453.11096

Math. Notes 107, No. 3, 404-412 (2020); translation from Mat. Zametki 107, No. 3, 366-375 (2020).
Let \(p, q_1, q_2, q_3\in\mathbb Z\) and \(H=\max_{1\leq i\leq 3} \mid q_i\mid\). Then the authors prove that there exists \(H_0\in\mathbb R\) such that for every \(H\geq H_0\) we have \[\mid p+q_1\ln 2+q_2\ln 3+q_3\ln 7\mid >H^{35,00999}.\]

MSC:

11J82 Measures of irrationality and of transcendence
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References:

[1] Wu, Q., On the linear independence measure of logarithms of rational numbers, Math. Comp., 72, 242, 901-911 (2002) · Zbl 1099.11037 · doi:10.1090/S0025-5718-02-01442-4
[2] Hata, M., Rational approximations to π and some other numbers, Acta Arith., 63, 4, 325-349 (1993) · Zbl 0776.11033 · doi:10.4064/aa-63-4-335-349
[3] Salikhov, V. Kh, On the irrationality measure of In 3, Dokl. Akad. Nauk, 417, 6, 753-755 (2007) · Zbl 1169.11032
[4] Wu, Q.; Wang, L., On the irrationality measure of log 3, J. Number Theory, 142, 264-273 (2014) · Zbl 1303.11081 · doi:10.1016/j.jnt.2014.03.007
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