Some field theoretic properties and an application concerning transcendental numbers

Chr Ulrik Jensen; Diego Marques

doi:10.1142/S0219498810004038

Some field theoretic properties and an application concerning transcendental numbers

Chr Ulrik Jensen, Diego Marques

Department of Mathematical Sciences

4 Citations (Scopus)

Abstract

For a proper subfield K of ℚ̄ 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 ℚ̄.

Original language	English
Journal	Journal of Algebra and its Applications
Volume	9
Issue number	3
Pages (from-to)	493-500
Number of pages	8
ISSN	0219-4988
DOIs	https://doi.org/10.1142/S0219498810004038
Publication status	Published - Jun 2010

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Jensen, C. U., & Marques, D. (2010). Some field theoretic properties and an application concerning transcendental numbers. Journal of Algebra and its Applications, 9(3), 493-500. https://doi.org/10.1142/S0219498810004038

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AB - For a proper subfield K of ℚ̄ 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 ℚ̄.

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DO - 10.1142/S0219498810004038

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Some field theoretic properties and an application concerning transcendental numbers

Abstract

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