Analytic continuation of the Lucas zeta and \(L\)-functions

DOI10.1016/J.INDAG.2013.04.002zbMath1282.11118OpenAlexW2044919064MaRDI QIDQ391072

Ken Kamano

Publication date: 9 January 2014

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2013.04.002

zbMATH Keywords

Lucas sequencesDirichlet's \(L\)-functionsFibonacci zeta function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Recurrences (11B37) Other Dirichlet series and zeta functions (11M41) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (9)

On the finite reciprocal sums of Fibonacci and Lucas polynomials ⋮ The zeta function of a recurrence sequence of arbitrary degree ⋮ The Tribonacci Dirichlet series ⋮ On the zeros of the partial sums of the Fibonacci zeta function ⋮ Dynamics of a family of continued fraction maps ⋮ Multiple Lucas-Dirichlet series associated with additive and Dirichlet characters ⋮ On Lucas-balancing zeta function ⋮ Analytic continuation of the multiple Lucas zeta functions ⋮ Unnamed Item

Cites Work

• Asymptotic representations for Fibonacci reciprocal sums and Euler's formulas for zeta values
• Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers
• Algebraic independence results for reciprocal sums of Fibonacci numbers
• Algebraic relations for reciprocal sums of Fibonacci numbers
• Number Theory
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