### Abstract

Suppose that {R_{n}}_{n≥0} is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers ∑′_{k ≥ 0} a^{k}/R_{cd(k)} + b′ where a is a nonzero algebraic number and b, c, and d are integers with c ≥ 1 and d ≥ 2, and that of similarly constructed numbers, using a new theorem on the transcendence of functions.

Original language | English |
---|---|

Pages (from-to) | 115-128 |

Number of pages | 14 |

Journal | Monatshefte fur Mathematik |

Volume | 137 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2002 Oct |

Externally published | Yes |

### Fingerprint

### Keywords

- Transcendence, Mahler functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Monatshefte fur Mathematik*,

*137*(2), 115-128. https://doi.org/10.1007/s00605-002-0501-4

**Transcendence of certain reciprocal sums of linear recurrences.** / Duverney, Daniel; Kanoko, Tomoaki; Tanaka, Takaaki.

Research output: Contribution to journal › Article

*Monatshefte fur Mathematik*, vol. 137, no. 2, pp. 115-128. https://doi.org/10.1007/s00605-002-0501-4

}

TY - JOUR

T1 - Transcendence of certain reciprocal sums of linear recurrences

AU - Duverney, Daniel

AU - Kanoko, Tomoaki

AU - Tanaka, Takaaki

PY - 2002/10

Y1 - 2002/10

N2 - Suppose that {Rn}n≥0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers ∑′k ≥ 0 ak/Rcd(k) + b′ where a is a nonzero algebraic number and b, c, and d are integers with c ≥ 1 and d ≥ 2, and that of similarly constructed numbers, using a new theorem on the transcendence of functions.

AB - Suppose that {Rn}n≥0 is a sequence of integers satisfying a binary linear recurrence relation with suitable conditions. We prove the transcendency of the numbers ∑′k ≥ 0 ak/Rcd(k) + b′ where a is a nonzero algebraic number and b, c, and d are integers with c ≥ 1 and d ≥ 2, and that of similarly constructed numbers, using a new theorem on the transcendence of functions.

KW - Transcendence, Mahler functions

UR - http://www.scopus.com/inward/record.url?scp=0036776268&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036776268&partnerID=8YFLogxK

U2 - 10.1007/s00605-002-0501-4

DO - 10.1007/s00605-002-0501-4

M3 - Article

AN - SCOPUS:0036776268

VL - 137

SP - 115

EP - 128

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 2

ER -