Transcendence of certain reciprocal sums of linear recurrences

Daniel Duverney; Tomoaki Kanoko; Taka Aki Tanaka

doi:10.1007/s00605-002-0501-4

Transcendence of certain reciprocal sums of linear recurrences

Daniel Duverney, Tomoaki Kanoko, Taka Aki Tanaka

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

10 Citations (Scopus)

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	https://doi.org/10.1007/s00605-002-0501-4
Publication status	Published - 2002 Oct 1
Externally published	Yes

Keywords

Transcendence, Mahler functions

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00605-002-0501-4

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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.

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ER -

Transcendence of certain reciprocal sums of linear recurrences

Abstract

Keywords

ASJC Scopus subject areas

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