{
  "id": "1807.03883",
  "version": "v1",
  "published": "2018-07-10T21:50:00.000Z",
  "updated": "2018-07-10T21:50:00.000Z",
  "title": "Apéry-like numbers and families of newforms with complex multiplication",
  "authors": [
    "Alexis Gomez",
    "Dermot McCarthy",
    "Dylan Young"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Using Hecke characters, we construct two infinite families of newforms with complex multiplication, one by $\\mathbb{Q}(\\sqrt{-3})$ and the other by $\\mathbb{Q}(\\sqrt{-2})$. The values of the $p$-th Fourier coefficients of all the forms in each family can be described by a single formula, which we provide explicitly. This allows us to establish a formula relating the $p$-th Fourier coefficients of forms of different weights, within each family. We then prove congruence relations between the $p$-th Fourier coefficients of these newforms at all odd weights and values coming from two of Zagier's sporadic Ap\\'ery-like sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-10T21:50:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex multiplication",
      "th fourier coefficients",
      "apéry-like numbers",
      "zagiers sporadic apery-like sequences",
      "hecke characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}