Transcendence of certain reciprocal sums of linear recurrences

Daniel Duverney, Tomoaki Kanoko, Taka Aki Tanaka

Research output: Contribution to journalArticle

9 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 languageEnglish
Pages (from-to)115-128
Number of pages14
JournalMonatshefte fur Mathematik
Volume137
Issue number2
DOIs
Publication statusPublished - 2002 Oct 1
Externally publishedYes

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Keywords

  • Transcendence, Mahler functions

ASJC Scopus subject areas

  • Mathematics(all)

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