English

Analytic continuation of $\ell$-generalized Fibonacci zeta function

Number Theory 2023-05-26 v1

Abstract

In this paper, for any positive integer 2,\ell\geq2, we define \ell-generalized Fibonacci zeta function. We then study its analytic continuation to the whole complex plane C.\mathbb{C}. Further, we compute a possible list of singularities and residues of the function at these simple poles. Moreover, we deduce that the special values of \ell-generalized Fibonacci zeta function at negative integer arguments are rational.

Keywords

Cite

@article{arxiv.2305.16184,
  title  = {Analytic continuation of $\ell$-generalized Fibonacci zeta function},
  author = {Dilip Kumar Sahoo and Nabin Kumar Meher},
  journal= {arXiv preprint arXiv:2305.16184},
  year   = {2023}
}
R2 v1 2026-06-28T10:46:13.891Z