某些三角级数的超越性

朱尧辰

数学学报 ›› 2005, Vol. 48 ›› Issue (3) : 605-608.

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数学学报 ›› 2005, Vol. 48 ›› Issue (3) : 605-608. DOI: 10.12386/A2005sxxb0075
论文

某些三角级数的超越性

    朱尧辰
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Transcendence of Certain Trigonometric Series

    Yao Chen ZHU
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摘要

本文在仅与系数有关的一般条件下证明了某些代数系数三角级数及其导数在代数点上值的超越性.定理的证明基于一个关于数域上的线性无关性的判别法则.

Abstract

In this paper the transcendence of values of certain trigonometric series with algebraic coefficients and its derivatives at algebraic points is proved under a general condition dependent only on the coefficients. The proof of the theorem is based on a criterion for linear independence over a number field.

关键词

超越性 / 三角级数 / 线性无关性 / 数域

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朱尧辰. 某些三角级数的超越性. 数学学报, 2005, 48(3): 605-608 https://doi.org/10.12386/A2005sxxb0075
Yao Chen ZHU. Transcendence of Certain Trigonometric Series. Acta Mathematica Sinica, Chinese Series, 2005, 48(3): 605-608 https://doi.org/10.12386/A2005sxxb0075
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