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Mat. Sb., 2019, Volume 210, Number 12, Pages 136–150 (Mi msb9145)  

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

Abstract: 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.

DOI: https://doi.org/10.4213/sm9145

Full text: PDF file (559 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2019, 210:12, 1788–1802

Bibliographic databases:

UDC: 511.6+517.547.22
MSC: Primary 11J91; Secondary 30D15
Received: 04.07.2018 and 10.04.2019

Citation: 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
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  • https://doi.org/10.4213/sm9145
  • http://mi.mathnet.ru/eng/msb/v210/i12/p136

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  • Математический сборник Sbornik: Mathematics (from 1967)
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