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arXiv · 2412.13620

The Fibonacci Zeta Function and Continuation

Eran Assaf·Chan Ieong Kuan·David Lowry-Duda·Alexander Walker
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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.

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Eran Assaf, Chan Ieong Kuan, David Lowry-Duda, Alexander Walker. 2024-12-18. The Fibonacci Zeta Function and Continuation. https://arxiv.org/abs/2412.13620

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