Algebraic independence results for reciprocal sums of Fibonacci numbers

DOI10.4064/aa148-3-1zbMath1231.11080OpenAlexW2324485441MaRDI QIDQ2994982

Iekata Shiokawa, Carsten Elsner, Shun Shimomura

Publication date: 29 April 2011

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/ea315a3a601e385d5f0887ef825ea347bbf3f350

zbMATH Keywords

Fibonacci numbersalgebraic independenceRamanujan q-series

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Transcendence (general theory) (11J81) Algebraic numbers; rings of algebraic integers (11R04) Elliptic functions and integrals (33E05)

Related Items (17)

The reciprocal sums of even and odd terms in the Fibonacci sequence ⋮ On the reciprocal sums of higher-order sequences ⋮ On algebraic relations for Ramanujan's functions ⋮ Analytic continuation of the Lucas zeta and \(L\)-functions ⋮ Several identities involving the Fibonacci polynomials and Lucas polynomials ⋮ Algebraic independence of values of quasi-modular forms ⋮ Algebraic results for the values \(\vartheta_3(m\tau)\) and \(\vartheta_3(n\tau)\) of the Jacobi theta-constant ⋮ Algebraic independence of subseries over arithmetical progressions of certain exponential power series ⋮ Algebraic results for certain values of the Jacobi theta-constant $\theta_3(\tau)$ ⋮ Sums of products of two reciprocal Fibonacci numbers ⋮ On the partial finite sums of the reciprocals of the Fibonacci numbers ⋮ A remark on Nesterenko's theorem for Ramanujan functions ⋮ Algebraic independence of certain numbers related to modular functions ⋮ The reciprocal sums of the Fibonacci 3-subsequences ⋮ ON LINEAR RELATIONS FOR DIRICHLET SERIES FORMED BY RECURSIVE SEQUENCES OF SECOND ORDER ⋮ The Fibonacci sequence and an elliptic curve ⋮ Algebraic independence results for values of theta-constants

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