Algebraic relations for reciprocal sums of Fibonacci numbers
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Publication:5423576
DOI10.4064/aa130-1-3zbMath1132.11036OpenAlexW1999081991MaRDI QIDQ5423576
Iekata Shiokawa, Carsten Elsner, Shun Shimomura
Publication date: 23 October 2007
Published in: Acta Arithmetica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4064/aa130-1-3
Transcendence theory of other special functions (11J91) Transcendence (general theory) (11J81) Elliptic functions and integrals (33E05)
Related Items (19)
The reciprocal sums of even and odd terms in the Fibonacci sequence ⋮ Balancing Dirichlet series and related \(L\)-functions ⋮ Analytic continuation of the Lucas zeta and \(L\)-functions ⋮ Algebraic independence of values of quasi-modular forms ⋮ Sums of products of two reciprocal Fibonacci numbers ⋮ Multiple Lucas-Dirichlet series associated with additive and Dirichlet characters ⋮ Algebraic relations for reciprocal sums of even terms in 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 ⋮ Analytic continuation of the multiple Fibonacci zeta functions ⋮ Algebraic independence results for the sixteen families of \(q\)-series ⋮ On Lucas-balancing zeta function ⋮ Analytic continuation of the multiple Lucas zeta functions ⋮ The reciprocal sums of the Fibonacci 3-subsequences ⋮ Unnamed Item ⋮ Asymptotic representations for Fibonacci reciprocal sums and Euler's formulas for zeta values ⋮ ON LINEAR RELATIONS FOR DIRICHLET SERIES FORMED BY RECURSIVE SEQUENCES OF SECOND ORDER ⋮ The Fibonacci sequence and an elliptic curve
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