{
  "id": "1604.04918",
  "version": "v1",
  "published": "2016-04-17T19:59:12.000Z",
  "updated": "2016-04-17T19:59:12.000Z",
  "title": "New realizations of modular forms in Calabi-Yau threefolds arising from $φ^4$ theory",
  "authors": [
    "Adam Logan"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "It has been found experimentally by Brown and Schnetz that the number of points over ${\\mathbb F}_p$ of a graph hypersurface is often related to the coefficients of a modular form. In this paper I prove this relation for one example of a modular form of weight $4$ and two of weight $3$, refine the statement and suggest a method of proving it for four more of weight $4$, and use the one proved example to construct two new rigid Calabi-Yau threefolds that realize Hecke eigenforms of weight $4$ (one provably and one conjecturally).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-17T19:59:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "11F11",
      "11F23",
      "14E15",
      "81Q30"
    ],
    "keywords": [
      "modular form",
      "calabi-yau threefolds arising",
      "realizations",
      "rigid calabi-yau threefolds",
      "graph hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404918L",
      "inspire": 1448347
    }
  }
}