Transcendence of infinite products involving Fibonacci and Lucas numbers

DOI10.1007/s40993-022-00366-1zbMath1504.11083OpenAlexW4295836564WikidataQ114217978 ScholiaQ114217978MaRDI QIDQ2674250

Takeshi Kurosawa, Daniel Duverney

Publication date: 22 September 2022

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40993-022-00366-1

zbMATH Keywords

transcendenceFibonacci numbersLucas numbersinfinite productsgolden ratioMahler's method

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Transcendence (general theory) (11J81)

Related Items (1)

Algebraic and arithmetical properties of Mahler infinite products generated by the second degree polynomials

Cites Work

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• On algebraic independence of a class of infinite products
• Applications of a transcendence criterion for reciprocal sums of binary linear recurrences
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• Transcendence of certain series involving binary linear recurrences
• Transcendence of certain infinite products
• Transcendence criterion for values of certain functions of several variables
• Algebraic independence of certain Mahler functions
• Arithmetical properties of certain infinite products
• Algebraic independence results for the values of certain Mahler functions and their application to infinite products
• An inductive method for proving the transcendence of certain series
• Transcendency Results for Sums of Reciprocals of Linear Recurrences
• Explicit algebraic dependence formulae for infinite products related with Fibonacci and Lucas numbers

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