Some arithmetic properties of the values of entire functions of finite order and their first derivatives
A. Ya. Yanchenko
National Research University "Moscow Power Engineering Institute", Moscow, Russia
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.
entire function of finite order, derivative, algebraic values, exponentials.
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Sbornik: Mathematics, 2019, 210:12, 1788–1802
MSC: Primary 11J91; Secondary 30D15
Received: 04.07.2018 and 10.04.2019
A. Ya. Yanchenko, “Some arithmetic properties of the values of entire functions of finite order and their first derivatives”, Mat. Sb., 210:12 (2019), 136–150; Sb. Math., 210:12 (2019), 1788–1802
Citation in format AMSBIB
\paper Some arithmetic properties of the values of entire functions of finite order and their first derivatives
\jour Mat. Sb.
\jour Sb. Math.
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