This article is cited in 5 scientific papers (total in 5 papers)
On estimates for the orders of zeros of polynomials in analytic functions and their application to estimates for the relative transcendence measure of values of E-functions
Abstract:
This paper gives estimates for the orders of zeros of polynomials in a set of analytic functions satisfying a system of linear differential equations with coefficients in C(z), in the case when these functions are algebraically dependent over C(z). Using the Siegel–Shidlovskii method, these estimates are applied to obtain effective bounds from below for the relative transcendence measure of the values of E-functions in the case when the basic set of E-functions is algebraically dependent over C(z).
Bibliography: 20 titles.
Citation:
Nguyen Tien Tai, “On estimates for the orders of zeros of polynomials in analytic functions and their application to estimates for the relative transcendence measure of values of E-functions”, Math. USSR-Sb., 48:1 (1984), 111–140
\Bibitem{Ngu83}
\by Nguyen Tien Tai
\paper On estimates for the orders of zeros of polynomials in analytic functions and their application to estimates for the relative transcendence measure of values of $E$-functions
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 1
\pages 111--140
\mathnet{http://mi.mathnet.ru/eng/sm2108}
\crossref{https://doi.org/10.1070/SM1984v048n01ABEH002664}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=687339}
\zmath{https://zbmath.org/?q=an:0542.10027|0516.10025}
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https://doi.org/10.1070/SM1984v048n01ABEH002664
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This publication is cited in the following 5 articles:
Zorin E., “Multiplicity Estimates For Algebraically Dependent Analytic Functions”, Proc. London Math. Soc., 108:4 (2014), 989–1029
A. P. Dolgalev, “Estimates for the Orders of Zeros of Polynomials in Some Analytic Functions”, Math. Notes, 84:2 (2008), 184–196
W. V. Zudilin, “On rational approximations of values of a certain class of entire functions”, Sb. Math., 186:4 (1995), 555–590
Zhukov A., “On Effective Estimation of Zero Order for a Polynomial Over a Set of Functions Satisfying a Linear-Differential Equations System”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1991, no. 1, 79–82
W. Dale Brownawell, “Effectivity in independence measures for values of E-functions”, J Austral Math Soc, 39:2 (1985), 227
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