Transcendence of certain reciprocal sums of linear recurrences

Daniel Duverney, Tomoaki Kanoko, Taka Aki Tanaka

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2002 Oct 1
Externally publishedYes


  • Transcendence, Mahler functions

ASJC Scopus subject areas

  • General Mathematics


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