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

Institut for Matematiske Fag

4 Citationer (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.

Originalsprog	Engelsk
Tidsskrift	Journal of Algebra and its Applications
Vol/bind	9
Udgave nummer	3
Sider (fra-til)	493-500
Antal sider	8
ISSN	0219-4988
DOI	https://doi.org/10.1142/S0219498810004038
Status	Udgivet - jun. 2010

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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.

U2 - 10.1142/S0219498810004038

DO - 10.1142/S0219498810004038

M3 - Journal article

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VL - 9

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JO - Journal of Algebra and its Applications

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IS - 3

ER -

Some field theoretic properties and an application concerning transcendental numbers

Abstract

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