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 $\mathbf C(z)$, in the case when these functions are algebraically dependent over $\mathbf C(z)$. 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 $\mathbf C(z)$.
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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