{
  "abstract": "Let $F_1=F_2=1$, $F_{n+2}=F_{n+1}+F_n$, and define the Fibonacci zeta function by $$ Z_F(s)=\\sum_{n\\ge1}F_n^{-s},\\qquad \\operatorname{Re}s>0. $$ We determine the exact right edge of the closure of the real parts of its zeros in the half-plane of absolute convergence. If $σ_F$ is the unique solution of $$ Z_F(σ_F)=4+2\\,144^{-σ_F}, $$ then $$ σ_F=0.743163398726901648\\ldots, $$ $Z_F(s)\\neq0$ for $\\operatorname{Re}s\\geσ_F$, while $$ \\overline{\\{\\operatorname{Re}ρ:Z_F(ρ)=0,\\ \\operatorname{Re}ρ>0\\}}=[0,σ_F]. $$ The edge is sharp in an almost-periodic sense: zeros occur with relatively dense ordinates near every admissible vertical line. We prove growing-dimensional phase locking near the edge and a Diophantine zero-free cusp, and describe the associated Jessen function and smooth mean vertical zero density. For every partial sum with $N\\ge12$ we determine the corresponding exact closure edge $σ_N$, prove $σ_N\\nearrowσ_F$, and obtain an exponential asymptotic for $σ_F-σ_N$. We also derive a finite-core theorem for positive integral Lucas zeta functions, with the Pell zeta function as an explicit example. Finally, using the known meromorphic continuation, we construct a natural $q$-Pochhammer completion that is entire of exact order $2$ and type $\\logφ/4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04993",
  "author_total": 1,
  "authors": [
    {
      "name": "Marco Mantovanelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5vmrt2aderaz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04993",
  "fulltext_url": null,
  "id": "b5vmrt2aderaz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04993",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7211879383",
  "pdf_url": "https://arxiv.org/pdf/2609.04993",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5vmrt2aderaz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04993",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04993"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Right Edge of the Zero Set of the Fibonacci Zeta Function",
  "title_text": "The Right Edge of the Zero Set of the Fibonacci Zeta Function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/b5vmrt2aderaz",
  "venue": "arXiv",
  "versions": []
}