{
  "abstract": "It is a popular paradoxical exercise to show that the infinite sum of positive integer numbers is equal to –1/12, sometimes called the Ramanujan sum. This result is actually well-defined in a proper mathematical sense. Here we propose a qualitative approach, much like that of a physicist, to show how the value –1/12 can make sense and, in fact, appears in certain physical quantities where this type of summation is involved. At the light of two physical examples, taken respectively from condensed matter – the Landau diamagnetism – and quantum electrodynamics – the Casimir effect – that illustrate this strange sum, we present a systematic way to extract this Ramanujan term from the infinity. In both examples, the “infinite” appears to be a vacuum energy and the Ramanujan sum is revealed by a response function to an external parameter.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2506.08664",
  "author_total": 1,
  "authors": [
    {
      "name": "Gilles Montambaux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1htd5c9e0w7g1.bib",
  "cited_by": 1,
  "doi": "10.5802/crphys.256",
  "fulltext_url": null,
  "id": "1htd5c9e0w7g1",
  "issns": [
    "1631-0705",
    "1878-1535"
  ],
  "landing_url": "https://hal.science/hal-05853598v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.phys"
    ],
    [
      "openalex",
      "3107|Quantum Electrodynamics and Casimir Effect"
    ]
  ],
  "openalex": "W4412903258",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": "Académie des sciences (Paris)",
  "ris": "https://research.draconitic.com/paper/1htd5c9e0w7g1.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:44Z",
      "native_id": "hal-05853598",
      "source": "hal",
      "url": "https://hal.science/hal-05853598v1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Quantum Electrodynamics and Casimir Effect",
      "subfield": "amo"
    }
  ],
  "title": "Ramanujan, Landau et Casimir, les séries divergentes: l’approche d’un physicien",
  "title_text": "Ramanujan, Landau et Casimir, les séries divergentes: l’approche d’un physicien",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T12:20:25Z",
  "url": "https://research.draconitic.com/paper/1htd5c9e0w7g1",
  "venue": "Comptes Rendus. Physique",
  "versions": []
}