Hokkaido Mathematical Journal

Algebraic independence of infinite products generated by Fibonacci and Lucas numbers

Florian LUCA and Yohei TACHIYA

Full-text: Open access

Abstract

The aim of this paper is to give an algebraic independence result for the two infinite products involving the Lucas sequences of the first and second kind. As a consequence, we derive that the two infinite products ∏k=1(1+1/F2k) and ∏k=1(1+1/L2k) are algebraically independent over ℚ, where {Fn}n≥0 and {Ln}n≥0 are the Fibonacci sequence and its Lucas companion, respectively.

Article information

Source
Hokkaido Math. J., Volume 43, Number 1 (2014), 1-20.

Dates
First available in Project Euclid: 20 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1392906090

Digital Object Identifier
doi:10.14492/hokmj/1392906090

Mathematical Reviews number (MathSciNet)
MR3072299

Zentralblatt MATH identifier
1291.11103

Subjects
Primary: 11J85: Algebraic independence; Gelʹfond's method 11B39: Fibonacci and Lucas numbers and polynomials and generalizations

Keywords
Infinite products algebraic independence Mahler-type functional equation Fibonacci numbers

Citation

LUCA, Florian; TACHIYA, Yohei. Algebraic independence of infinite products generated by Fibonacci and Lucas numbers. Hokkaido Math. J. 43 (2014), no. 1, 1--20. doi:10.14492/hokmj/1392906090. https://projecteuclid.org/euclid.hokmj/1392906090


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