{
  "abstract": "Let \\(N_M(λ)\\) be the spectral counting function of the sub-Laplacian on the compact Heisenberg manifold \\(M=Γ\\backslash\\mathbb H_d\\), where $Γ$ is a lattice subgroup of the Heisenberg group $\\mathbb H_d$. In 2016, Strichartz \\cite[\\textit{J. Geom. Anal.}]{Str16} proved the Weyl law with remainder \\(R_M(λ)=N_M(λ)-A_d\\operatorname{vol}(M)λ^{d+1} = O_M(λ^d\\logλ)\\), and conjectured the optimal remainder to be \\(O_M(λ^d)\\). In this work, we establish a new upper bound and the first two-sided lower bounds $$ R_M(λ)=O_M\\!\\left(λ^d(\\logλ)^{2/3}\\right), \\qquad R_M(λ)=Ω_{M,\\pm}\\!\\left(λ^d\\log\\logλ\\right). $$ As a result, this implies that the sharp polynomial order is $d$, and disproves Strichartz's conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08309",
  "author_total": 2,
  "authors": [
    {
      "name": "Sheng-Chen Mao"
    },
    {
      "name": "Ye Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53qqafafm471z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08309",
  "fulltext_url": null,
  "id": "53qqafafm471z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08309",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7212087236",
  "pdf_url": "https://arxiv.org/pdf/2609.08309",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53qqafafm471z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08309",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08309"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spectral asymptotics of sub-Riemannian Laplacians on compact Heisenberg manifolds",
  "title_text": "Spectral asymptotics of sub-Riemannian Laplacians on compact Heisenberg manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/53qqafafm471z",
  "venue": "arXiv",
  "versions": []
}