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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title = "Some field theoretic properties and an application concerning transcendental numbers",

abstract = "For a proper subfield K of {\=ℚ} 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 {\=ℚ}.",

author = "Jensen, {Chr Ulrik} and Diego Marques",

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AU - Marques, Diego

PY - 2010/6

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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

SN - 0219-4988

VL - 9

SP - 493

EP - 500

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

IS - 3

ER -

Some field theoretic properties and an application concerning transcendental numbers

Abstract

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