{
  "id": "1402.1854",
  "version": "v2",
  "published": "2014-02-08T14:09:05.000Z",
  "updated": "2016-01-17T10:55:09.000Z",
  "title": "Periods of modular forms and identities between Eisenstein series",
  "authors": [
    "Kamal Khuri-Makdisi",
    "Wissam Raji"
  ],
  "comment": "16 pages, amslatex. Version 2: some minor edits",
  "categories": [
    "math.NT"
  ],
  "abstract": "Borisov and Gunnells observed in 2001 that certain linear relations between products of two holomorphic weight 1 Eisenstein series had the same structure as the relations between periods of modular forms; a similar phenomenon exists in higher weights. We give a conceptual reason for this observation in arbitrary weight. This involves an unconventional way of expanding the Rankin-Selberg convolution of a cusp form with an Eisenstein series. We also prove a partial result towards understanding the action of a Hecke operator on a product of two Eisenstein series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-08T14:09:05.000Z",
      "abstract": "Borisov and Gunnells observed in 2001 that certain linear relations between products of two holomorphic weight 1 Eisenstein series had the same structure as the relations between periods of modular forms; a similar phenomenon exists in higher weights. We give a conceptual reason for this observation in arbitrary weight. This involves an unconventional way of expanding the Rankin-Selberg convolution of a cusp form with an Eisenstein series.",
      "comment": "16 pages, amslatex",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-01-17T10:55:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F11"
    ],
    "keywords": [
      "eisenstein series",
      "modular forms",
      "identities",
      "higher weights",
      "holomorphic weight"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.1854K"
    }
  }
}