Geodesic
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
Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 111-140 
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. Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 111-140. http://geodesic.mathdoc.fr/item/SM_1984_48_1_a5/
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     author = {Nguyen Tien Tai},
     title = {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},
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     url = {http://geodesic.mathdoc.fr/item/SM_1984_48_1_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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