### Abstract

Algebraic independence of the numbers ∑^{l}_{h≥0}b_{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 |

Publication status | Published - 1999 |

### Fingerprint

### Keywords

- Algebraic independence
- Fibonacci numbers
- Mahler function

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematische Nachrichten*,

*202*, 97-108.

**Algebraic independence of sums of reciprocals of the Fibonacci numbers.** / Nishioka, Kumiko; Tanaka, Takaaki; Toshimitsu, Takeshi.

Research output: Contribution to journal › Article

*Mathematische Nachrichten*, vol. 202, pp. 97-108.

}

TY - JOUR

T1 - Algebraic independence of sums of reciprocals of the Fibonacci numbers

AU - Nishioka, Kumiko

AU - Tanaka, Takaaki

AU - Toshimitsu, Takeshi

PY - 1999

Y1 - 1999

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

UR - http://www.scopus.com/inward/record.url?scp=0010099829&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010099829&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0010099829

VL - 202

SP - 97

EP - 108

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

ER -