Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion

Taka Aki Tanaka

doi:10.1016/j.jnt.2003.09.010

Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion

Taka Aki Tanaka

数理科学科

研究成果: Article › 査読

2 被引用数 (Scopus)

抄録

It is proved that the function (a formula is presented), which can be expressed as a certain continued fraction, takes algebraically independent values at any distinct nonzero algebraic numbers inside the unit circle if the sequence {R_k}_k≥0 is the generalized Fibonacci numbers.

本文言語	English
ページ（範囲）	38-48
ページ数	11
ジャーナル	Journal of Number Theory
巻	105
号	1
DOI	https://doi.org/10.1016/j.jnt.2003.09.010
出版ステータス	Published - 2004 3月

ASJC Scopus subject areas

代数と数論

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10.1016/j.jnt.2003.09.010

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title = "Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion",

abstract = "It is proved that the function (a formula is presented), which can be expressed as a certain continued fraction, takes algebraically independent values at any distinct nonzero algebraic numbers inside the unit circle if the sequence {Rk}k≥0 is the generalized Fibonacci numbers.",

keywords = "Algebraic independence, Continued fractions, Fibonacci numbers, Mahler functions",

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KW - Algebraic independence

KW - Continued fractions

KW - Fibonacci numbers

KW - Mahler functions

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Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion

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