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Lower bounds of linear forms of values of G functions

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Abstract

Lower bounds are obtained for linear forms of values of Siegel's G functions. In particular, it is found that ifα 1...,α m are pairwise distinct nonzero rational numbers, then for any positive ɛ and a natural q>q0(ɛ,α 1,...,α m) we have for any nonzero set (x0 x1,..., xm) of integers the inequality

$$|x_0 + x_1 In(i + a_1 q^{ - 1} ) + ... + x_m In(i + a_m q^{ - 1} )|q^{ - \lambda } (h_1 ...h_m )^{ - 1 - \varepsilon } ,$$

where hi=max(i, ¦xi¦), andλ=λ (ɛ,α 1,...,α m).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. I. Galochkin

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  1. A. I. Galochkin
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Translated from Matematicheskie Zametki, Vol. 18, No. 4, pp. 541–552, October, 1975.

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Galochkin, A.I. Lower bounds of linear forms of values of G functions. Mathematical Notes of the Academy of Sciences of the USSR 18, 911–917 (1975). https://doi.org/10.1007/BF01153043

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  • DOI: https://doi.org/10.1007/BF01153043

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