Analytic continuation of $\ell$-generalized Fibonacci zeta function
Number Theory
2023-05-26 v1
Abstract
In this paper, for any positive integer we define -generalized Fibonacci zeta function. We then study its analytic continuation to the whole complex plane 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 -generalized Fibonacci zeta function at negative integer arguments are rational.
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}
}