Algebraic independence of sums of reciprocals of the Fibonacci numbers

Kumiko Nishioka; Taka Aki Tanaka; Takeshi Toshimitsu

doi:10.1002/mana.19992020108

Algebraic independence of sums of reciprocals of the Fibonacci numbers

Kumiko Nishioka, Taka Aki Tanaka, Takeshi Toshimitsu

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Algebraic independence of the numbers ∑^l_h≥0b_h/(R_kdh+l)^m, where {R_n}_n≥0 is a sequence of integers satisfying a binary linear recurrence relation and {b_h}_h≥0 is a periodic sequence of algebraic numbers not identically zero, are studied.

Original language	English
Pages (from-to)	97-108
Number of pages	12
Journal	Mathematische Nachrichten
Volume	202
DOIs	https://doi.org/10.1002/mana.19992020108
Publication status	Published - 1999 Jan 1

Keywords

Algebraic independence
Fibonacci numbers
Mahler function

ASJC Scopus subject areas

Mathematics(all)

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10.1002/mana.19992020108

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title = "Algebraic independence of sums of reciprocals of the Fibonacci numbers",

abstract = "Algebraic independence of the numbers ∑lh≥0bh/(Rkdh+l)m, where {Rn}n≥0 is a sequence of integers satisfying a binary linear recurrence relation and {bh}h≥0 is a periodic sequence of algebraic numbers not identically zero, are studied.",

keywords = "Algebraic independence, Fibonacci numbers, Mahler function",

author = "Kumiko Nishioka and Tanaka, {Taka Aki} and Takeshi Toshimitsu",

year = "1999",

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AU - Nishioka, Kumiko

AU - Tanaka, Taka Aki

AU - Toshimitsu, Takeshi

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Y1 - 1999/1/1

N2 - Algebraic independence of the numbers ∑lh≥0bh/(Rkdh+l)m, where {Rn}n≥0 is a sequence of integers satisfying a binary linear recurrence relation and {bh}h≥0 is a periodic sequence of algebraic numbers not identically zero, are studied.

AB - Algebraic independence of the numbers ∑lh≥0bh/(Rkdh+l)m, where {Rn}n≥0 is a sequence of integers satisfying a binary linear recurrence relation and {bh}h≥0 is a periodic sequence of algebraic numbers not identically zero, are studied.

KW - Algebraic independence

KW - Fibonacci numbers

KW - Mahler function

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Algebraic independence of sums of reciprocals of the Fibonacci numbers

Abstract

Keywords

ASJC Scopus subject areas

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