{
  "abstract": "The aim of this paper is to study the variation under quadratic twists of the analytic Iwasawa invariants of Sprung's sharp/flat 2-adic $L$-functions for elliptic curves over $\\mathbb{Q}$ with good supersingular reduction at $2$. Under the hypothesis that the $μ$-invariant vanishes, we obtain an explicit formula for the sharp/flat $λ$-invariants. This formula gives a supersingular analogue of Matsuno's formula in the good ordinary case. As an application, we show that the sharp/flat $λ$-invariants can be made arbitrarily large even among quadratic twists by single primes. Moreover, using the method of Hatley-Ray, we obtain an asymptotic lower bound for the number of quadratic twists with a prescribed sharp/flat 2-adic Iwasawa $λ$-invariant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.05305",
  "author_total": 1,
  "authors": [
    {
      "name": "Taiga Adachi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4wwfjfm3e88fb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.05305",
  "fulltext_url": null,
  "id": "4wwfjfm3e88fb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.05305",
  "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",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7167634167",
  "pdf_url": "https://arxiv.org/pdf/2607.05305",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4wwfjfm3e88fb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2607.05305",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.05305"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Iwasawa invariants of sharp/flat $2$-adic $L$-functions for quadratic twists of elliptic curves",
  "title_text": "Iwasawa invariants of sharp/flat $2$-adic L-functions for quadratic twists of elliptic curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/4wwfjfm3e88fb",
  "venue": "arXiv",
  "versions": []
}