Geodesic
Some arithmetic properties of the values of entire functions of finite order and their first derivatives
Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1788-1802 Cet article a éte moissonné depuis la source Math-Net.Ru

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We describe a class of entire functions of finite order which, together with their first derivative, take sufficiently many algebraic values (with certain restrictions on the growth of the degree and height of these values). We show that, under certain conditions, any such function is a rational function of special form of an exponential. For entire functions of finite order which are not representable in the form of a finite linear combination of exponentials, we obtain an estimate for the number of points (in any fixed disc) at which the values of the function itself and its first derivative are algebraic numbers of bounded degree and height. Bibliography: 8 titles.
Keywords: entire function of finite order, derivative, algebraic values, exponentials. 
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     title = {Some arithmetic properties of the values of entire functions of finite order and their first derivatives},
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A. Ya. Yanchenko. Some arithmetic properties of the values of entire functions of finite order and their first derivatives. Sbornik. Mathematics, Tome 210 (2019) no. 12, pp. 1788-1802. http://geodesic.mathdoc.fr/item/SM_2019_210_12_a6/

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