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Lower estimates for linear forms of $$G$$-function values. (English. Russian original) Zbl 0910.11030
Mosc. Univ. Math. Bull. 51, No. 3, 18-22 (1996); translation from Vestn. Mosk. Univ., Ser. I 1996, No. 3, 23-29 (1996).
The author establishes a lower estimate with integer coefficients from an imaginary quadratic field of $$G$$-function values. This estimate implies, in particular, that for any positive integer $$q > e^{131}$$, $1,\;\ln(1 - \tfrac 1q),\;\ln(1 + \tfrac 1q),\;\ln(1 - \tfrac 1q)\ln(1 + \tfrac 1q)$ are linearly independent over the field of rational numbers. The method of proving the basic result is close to the method applied by D. V. Chudnovsky and G. V. Chudnovsky [Lect. Notes Math. 1135, 9-51 (1985; Zbl 0561.10016)].
##### MSC:
 11J72 Irrationality; linear independence over a field 41A21 Padé approximation
##### Keywords:
$$G$$-functions; lower estimates of linear forms