Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers

DOI10.3792/pjaa.73.140zbMath0902.11029OpenAlexW2025211621MaRDI QIDQ1387932

Keiji Nishioka, Iekata Shiokawa, Kumiko Nishioka, Daniel Duverney

Publication date: 6 December 1998

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.73.140

zbMATH Keywords

transcendenceFibonacci sequenceLucas sequenceRogers-Ramanujan continued fraction

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Continued fractions and generalizations (11J70) Transcendence (general theory) (11J81) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items

Balancing Dirichlet series and related \(L\)-functions, Quantitative irrationality for sums of reciprocals of Fibonacci and Lucas numbers, Analytic continuation of the Lucas zeta and \(L\)-functions, Algebraic independence of values of quasi-modular forms, Dynamics of a family of continued fraction maps, Multiple Lucas-Dirichlet series associated with additive and Dirichlet characters, Algebraic relations for reciprocal sums of even terms in Fibonacci numbers, Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers, Analytic continuation of the multiple Fibonacci zeta functions, Analytic continuation of the multiple Lucas zeta functions, Unnamed Item, Elliptic Functions and Transcendence, Asymptotic representations for Fibonacci reciprocal sums and Euler's formulas for zeta values, On the spacings between \(C\)-nomial coefficients, ON LINEAR RELATIONS FOR DIRICHLET SERIES FORMED BY RECURSIVE SEQUENCES OF SECOND ORDER, The Fibonacci sequence and an elliptic curve, Irrationality measures for the series of reciprocals from recurrence sequences.

Cites Work

• On diophantine approximations of the Rogers-Ramanujan continued fraction
• Transcendence of Jacobi's theta series
• Rational approximations to the Rogers-Ramanujan continued fraction
• The Summation of Series of Hyperbolic Functions
• Modular functions and transcendence questions
• The Diophantine Approximation of Certain Continued Fractions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item