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Analytic continuation of $\ell$-generalized Fibonacci zeta function
- Publication Year :
- 2023
-
Abstract
- In this paper, for any positive integer $\ell\geq2,$ we define $\ell$-generalized Fibonacci zeta function. We then study its analytic continuation to the whole complex plane $\mathbb{C}.$ 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.
- Subjects :
- Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2305.16184
- Document Type :
- Working Paper