Algebraic Numbers as Product of Powers of Transcendental Numbers
Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic
Received: 17 June 2019 / Revised: 3 July 2019 / Accepted: 4 July 2019 / Published: 8 July 2019
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The elementary symmetric functions play a crucial role in the study of zeros of non-zero polynomials in
, and the problem of finding zeros in
leads to the definition of algebraic and transcendental numbers. Recently, Marques studied the set of algebraic numbers in the form
. In this paper, we generalize this result by showing the existence of algebraic numbers which can be written in the form
for some transcendental number T
are prescribed, non-constant polynomials in
(under weak conditions). More generally, our result generalizes results on the arithmetic nature of
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MDPI and ACS Style
Trojovský, P. Algebraic Numbers as Product of Powers of Transcendental Numbers. Symmetry 2019, 11, 887.
Trojovský P. Algebraic Numbers as Product of Powers of Transcendental Numbers. Symmetry. 2019; 11(7):887.
Trojovský, Pavel. 2019. "Algebraic Numbers as Product of Powers of Transcendental Numbers." Symmetry 11, no. 7: 887.
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