Štěpán Hubálovský, Eva Trojovská
Abstract
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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 αP(T), with T transcendental, is dense in some open interval of R.
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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 αP(T), with T transcendental, is dense in some open interval of R.
Key concepts: Transcendental number, Transcendental function, Algebraic extension, Algebraic number, Mathematics, Algebraic element, Algebraic function, Function field of an algebraic variety