{
  "abstract": "Let $\\Th(α,L)=\\sum_{v\\in L}e^{-πα|v|^2}$ for $α>0$ and $E(L,s)=\\sum_{v\\in L\\setminus\\{0\\}}|v|^{-2s}$ for $s>3/2$ be the theta and Epstein zeta functions associated to the lattice $L$, respectively. We are particularly interested in physically relevant dimension three. Fix the covolume of the lattice $L$ to $1$. Up to an orthogonal transformation, we prove that \\begin{equation}\\nonumber \\argmin_{|L|=1}\\Th(α,L)= \\begin{cases} \\boldsymbol{\\mathrm{FCC}}\\;\\;\\mathrm{lattice},\\;\\;\\;\\;\\;\\;\\;\\;\\; \\;\\;\\;\\;\\;\\;&\\text{if}\\;\\; α>1, \\boldsymbol{\\mathrm{BCC}}\\;\\;\\mathrm{lattice}, \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;&\\text{if}\\;\\; α<1, \\boldsymbol{\\mathrm{FCC}}\\;\\;\\mathrm{or}\\;\\; \\boldsymbol{\\mathrm{BCC}}\\;\\;\\mathrm{lattice},\\;\\;&\\text{if}\\;\\;α=1, \\end{cases} \\end{equation} and \\begin{equation}\\nonumber \\argmin_{|L|=1}E(L,s)= \\boldsymbol{\\mathrm{FCC}}\\;\\;\\mathrm{lattice},\\;\\;\\;\\;\\;\\;\\;\\;\\; \\;\\;\\;\\;\\;\\;\\text{if}\\;\\; s>3/2. \\end{equation} Therefore, we prove the Sarnak--Strömbergsson conjecture \\cite[Inequalities (43)--(44), Section 5]{SS}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17356",
  "author_total": 2,
  "authors": [
    {
      "name": "Senping Luo"
    },
    {
      "name": "Juncheng Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/047bx32jbkse1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17356",
  "fulltext_url": null,
  "id": "047bx32jbkse1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17356",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7213413614",
  "pdf_url": "https://arxiv.org/pdf/2609.17356",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/047bx32jbkse1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.17356",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17356"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On Sarnak--Strömbergsson conjecture",
  "title_text": "On Sarnak--Strömbergsson conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/047bx32jbkse1",
  "venue": "arXiv",
  "versions": []
}