Year: 2024
Type: preprint
Abstract: We introduce a family of Dirichlet series associated to real quadratic number fields that generalize the ordinary Fibonacci zeta function $\sum F(n)^{-s}$, where $F(n)$ denotes the $n$th Fibonacci number. We then give three different methods of meromorphic continuation to $\mathbb{C}$. Two are purely analytic and classical, while the third uses shifted convolutions and modular forms.
Source: arXiv (Cornell University)
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405626349