# Transcendence of certain reciprocal sums of linear recurrences

Daniel Duverney, Tomoaki Kanoko, Takaaki Tanaka

Research output: Contribution to journalArticle

8 Citations (Scopus)

### Abstract

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.

Original language English 115-128 14 Monatshefte fur Mathematik 137 2 https://doi.org/10.1007/s00605-002-0501-4 Published - 2002 Oct Yes

### Fingerprint

Linear Recurrence
Transcendence
Linear Recurrence Relation
Integer
Algebraic number
Binary
Theorem

### Keywords

• Transcendence, Mahler functions

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

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

In: Monatshefte fur Mathematik, Vol. 137, No. 2, 10.2002, p. 115-128.

Research output: Contribution to journalArticle

Duverney, Daniel ; Kanoko, Tomoaki ; Tanaka, Takaaki. / Transcendence of certain reciprocal sums of linear recurrences. In: Monatshefte fur Mathematik. 2002 ; Vol. 137, No. 2. pp. 115-128.
@article{e471ff46ea104553b9bf2b65a82ce4ab,
title = "Transcendence of certain reciprocal sums of linear recurrences",
abstract = "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.",
keywords = "Transcendence, Mahler functions",
author = "Daniel Duverney and Tomoaki Kanoko and Takaaki Tanaka",
year = "2002",
month = "10",
doi = "10.1007/s00605-002-0501-4",
language = "English",
volume = "137",
pages = "115--128",
journal = "Monatshefte fur Mathematik",
issn = "0026-9255",
publisher = "Springer Wien",
number = "2",

}

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 -