{
  "abstract": "Expander graphs have been central objects of study for over fifty years. Ramanujan graphs attain the asymptotically optimal nontrivial adjacency-eigenvalue threshold for infinite fixed-degree families. The original arithmetic constructions by Lubotzky-Phillips-Sarnak (1988) and Margulis (1988), and the iterative $2$-lift method of Bilu-Linial (2006) provide different approaches to Ramanujan graph constructions. Motivated by work on Mealy automata, we combine both approaches to give the following new arithmetic construction. For every prime $p\\equiv 1\\pmod {17}$, we construct a infinite tower of $(p+1)$-regular non-bipartite Ramanujan graphs on $2^n$ vertices, with label-preserving $2$-lifts between consecutive levels. These construction is strongly explicit: for fixed $p$, a neighbor or lift sign is computable in $O_p(n^3)$ bit operations. The construction uses fixed algebraic $2$-adic transformations, specified by finite data computable in preprocessing depending only on $p$. The main number-theoretic tool is Blasius's Ramanujan-Petersson theorem for Hilbert modular forms, applied through the Jacquet-Langlands correspondence to obtain the sharp bound $|λ|\\leq2\\sqrt p$ for every nontrivial adjacency eigenvalue of our $(p+1)$-regular graphs. The transformations preserve $2$-adic distance, which gives the binary covers and an explicit formula for their signings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39485",
  "author_total": 3,
  "authors": [
    {
      "name": "Olga Kharlampovich"
    },
    {
      "name": "Igor Pak"
    },
    {
      "name": "Alina Vdovina"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0aqnfc00q18v3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39485",
  "fulltext_url": null,
  "id": "0aqnfc00q18v3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39485",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0aqnfc00q18v3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Strongly explicit Ramanujan 2-lift towers via Hilbert modular forms",
  "title_text": "Strongly explicit Ramanujan 2-lift towers via Hilbert modular forms",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0aqnfc00q18v3",
  "venue": "arXiv",
  "versions": []
}