Tsukuba Journal of Mathematics

Algebraic independence of infinite products generated by Fibonacci numbers

Takeshi Kurosawa, Yohei Tachiya, and Taka-aki Tanaka

Full-text: Open access

Abstract

The aim of this paper is to establish necessary and sufficient conditions for certain infinite products generated by Fibonacci numbers and by Lucas numbers to be algebraically independent.

Article information

Source
Tsukuba J. Math., Volume 34, Number 2 (2011), 255-264.

Dates
First available in Project Euclid: 8 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1302268248

Digital Object Identifier
doi:10.21099/tkbjm/1302268248

Mathematical Reviews number (MathSciNet)
MR2808645

Zentralblatt MATH identifier
1218.11071

Subjects
Primary: 11J81: Transcendence (general theory) 11J85: Algebraic independence; Gelʹfond's method

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

Citation

Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Taka-aki. Algebraic independence of infinite products generated by Fibonacci numbers. Tsukuba J. Math. 34 (2011), no. 2, 255--264. doi:10.21099/tkbjm/1302268248. https://projecteuclid.org/euclid.tkbjm/1302268248


Export citation