Conditions for the algebraic independence of certain series involving continued fractions and generated by linear recurrences

DOI10.1016/j.jnt.2009.06.004zbMath1198.11062OpenAlexW2082014755MaRDI QIDQ1035598

Taka-aki Tanaka

Publication date: 4 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2009.06.004

zbMATH Keywords

continued fractionsFibonacci numbersalgebraic independenceMahler's method

Mathematics Subject Classification ID

Algebraic independence; Gel'fond's method (11J85) Continued fractions and generalizations (11J70)

Cites Work

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• Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion
• Proof of Masser's conjecture on the algebraic independence of values of Liouville series
• On the algebraic independence of holomorphic solutions of certain functional equations and their values
• Algebraic independence results related to linear recurrences
• Transcendental numbers. With a foreword by W. Dale Brownawell. Transl. from the Russian by Neal Koblitz
• Mahler functions and transcendence
• Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences
• Algebraic independence of the values of power series generated by linear recurrences

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