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SOME FIELD THEORETIC PROPERTIES AND AN APPLICATION CONCERNING TRANSCENDENTAL NUMBERS

CHRISTIAN U. JENSEN

Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

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and

DIEGO MARQUES

Departamento De Matemática, Universidade De Brasília, Brasília, DF, Brazil

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https://doi.org/10.1142/S0219498810004038Cited by:4 (Source: Crossref)

Abstract

For a proper subfield K of we show the existence of an algebraic number α such that no power αⁿ, n ≥ 1, lies in K. As an application it is shown that these numbers, multiplied by convenient Gaussian numbers, can be written in the form P(T)^Q(T) for some transcendental numbers T where P and Q are arbitrarily prescribed nonconstant rational functions over .

Keywords:

AMSC: 12F10, 11J81

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