Abstract:
Estimates from below are obtained for polynomials with integral coefficients in the values of certain Siegel G-functions at the algebraic points of a special form. In particular, it is proved that if α1,…,αs (α1⋯αs≠0) are pairwise distinct algebraic numbers, q is a natural number, and P(x1,…,xs)≢0 is a polynomial with integral coefficients of degree not greater than d and height not exceeding H, then for q>q0(d,α1,…,αs) we have
|P(ln(1+α1q),…,ln(1+αsq))|>q−λH−μ,
where the constants q0 and μ can be effectively computed.
Bibliography: 17 titles.
Citation:
A. I. Galochkin, “Estimates from below of polynomials in the values of analytic functions of a certain class”, Math. USSR-Sb., 24:3 (1974), 385–407
\Bibitem{Gal74}
\by A.~I.~Galochkin
\paper Estimates from below of polynomials in the values of analytic functions of a~certain class
\jour Math. USSR-Sb.
\yr 1974
\vol 24
\issue 3
\pages 385--407
\mathnet{http://mi.mathnet.ru/eng/sm3760}
\crossref{https://doi.org/10.1070/SM1974v024n03ABEH002190}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=357338}
\zmath{https://zbmath.org/?q=an:0311.10035}
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https://www.mathnet.ru/eng/sm3760
https://doi.org/10.1070/SM1974v024n03ABEH002190
https://www.mathnet.ru/eng/sm/v137/i3/p396
This publication is cited in the following 24 articles:
G. Lepetit, “Quantitative problems on the size of G-operators”, manuscripta math., 169:1-2 (2022), 51
Gabriel Lepetit, “On the linear independence of values of G-functions”, Journal of Number Theory, 219 (2021), 300
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posvyaschennoi 100-letiyu so dnya rozhdeniya professora Vyacheslava Timofeevicha Bazyleva.
Moskva, 22–25 aprelya 2019 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 179, VINITI RAN, M., 2020, 81–87
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