Transcendency Results for Sums of Reciprocals of Linear Recurrences

DOI10.1002/mana.19941680102zbMath0835.11026OpenAlexW2051428408MaRDI QIDQ4845807

Thomas Töpfer, P.-G. Becker-Landeck

Publication date: 24 October 1995

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19941680102

zbMATH Keywords

infinite seriesRoth's theoremtranscendencelinear recursive sequenceMahler's method

Mathematics Subject Classification ID

Recurrences (11B37) Transcendence (general theory) (11J81)

Related Items (11)

Algebraic Independence of Sums of Reciprocals of the Fibonacci Numbers ⋮ Transcendence of reciprocal sums of binary recurrences ⋮ Transcendence of the values of infinite products in several variables ⋮ Transcendence of certain series involving binary linear recurrences ⋮ Transcendence of infinite products involving Fibonacci and Lucas numbers ⋮ Algebraic independence results for the values of certain Mahler functions and their application to infinite products ⋮ Algebraic independence of reciprocal sums of binary recurrences ⋮ Algebraic independence of reciprocal sums of powers of certain Fibonacci-type numbers ⋮ Transcendental infinite sums ⋮ Transcendental series of reciprocals of Fibonacci and Lucas numbers ⋮ Irrationality results for reciprocal sums of certain Lucas numbers

Cites Work

• On the algebraic independence of holomorphic solutions of certain functional equations and their values
• Irrationality results for reciprocal sums of certain Lucas numbers
• The irrationality of certain infinite series
• On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.
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