Alexander Walker

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math.NT2024

The Fibonacci Zeta Function and Continuation

Eran Assaf, Chan Ieong Kuan, David Lowry-Duda +1

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…

math.NT2023

Counting Divisors in the Outputs of a Binary Quadratic Form

Chan Ieong Kuan, David Lowry-Duda, Alexander Walker +1

For a fixed natural number $h$ , we prove meromorphic continuation of the two-variable Dirichlet series $\sum_{m} r_{2} (m) σ_{w} (m + h) (m + h)^{- s + w}$ to $C^{2}$ and use this to…