{
  "id": "2006.11269",
  "version": "v1",
  "published": "2020-06-19T17:58:13.000Z",
  "updated": "2020-06-19T17:58:13.000Z",
  "title": "The Lang-Trotter Conjecture for products of non-CM elliptic curves",
  "authors": [
    "Hao Chen",
    "Nathan Jones",
    "Vlad Serban"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over $\\mathbb{Q}$ and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous question for abelian surfaces isogenous to products of non-CM elliptic curves over $\\mathbb{Q}$. We formulate the corresponding conjectural asymptotic, provide upper bounds, and explicitly compute (when the elliptic curves lie outside a thin set) the arithmetically significant constants appearing in the asymptotic. This allows us to provide computational evidence for the conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-19T17:58:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11F80"
    ],
    "keywords": [
      "non-cm elliptic curves",
      "lang-trotter conjecture",
      "elliptic curves lie outside",
      "generic abelian varieties",
      "fixed frobenius traces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}