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 Mat. Zametki, 2020, Volume 107, Issue 5, Pages 760–773 (Mi mz11242)

On a Class of Integer-Valued Functions

A. Y. Yanchenko*, V. A. Podkopaeva

National Research University "Moscow Power Engineering Institute"

Abstract: The paper deals with the class of entire functions that increase not faster than $\exp\{\gamma|z|^{6/5}(\ln|z|)^{-1}\}$ and that, together with their first derivatives, take values from a fixed field of algebraic numbers at the points of a two-dimensional lattice of general form (in this case, the values increase not too fast). It is shown that any such functions is either a polynomial or can be represented in the form $e^{-m\alpha z}P(e^{\alpha z})$, where $m$ is a nonnegative integer, $P$ is a polynomial, and $\alpha$ is an algebraic number.

Keywords: entire function, algebraic values.
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11242

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English version:
Mathematical Notes, 2020, 107:5, 826–837

Bibliographic databases:

UDC: 511.6+517.925
Revised: 19.11.2018

Citation: A. Y. Yanchenko, V. A. Podkopaeva, “On a Class of Integer-Valued Functions”, Mat. Zametki, 107:5 (2020), 760–773; Math. Notes, 107:5 (2020), 826–837

Citation in format AMSBIB
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