Algebraic Numbers of the form ? T with ? Algebraic and T Transcendental

Štěpán Hubálovský and Eva Trojovská
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Štěpán Hubálovský: Department of Applied Cybernetics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic
Eva Trojovská: Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic

Mathematics, 2020, vol. 8, issue 10, 1-6

Abstract: Let α ≠ 1 be a positive real number and let P ( x ) be a non-constant rational function with algebraic coefficients. In this paper, in particular, we prove that the set of algebraic numbers of the form α P ( T ) , with T transcendental, is dense in some open interval of R .

Keywords: Gelfond–Schneider theorem; algebraic numbers; transcendence; Schanuel’s conjecture (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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