{
  "id": "1509.04757",
  "version": "v1",
  "published": "2015-09-15T22:07:08.000Z",
  "updated": "2015-09-15T22:07:08.000Z",
  "title": "Representations of integers by systems of three quadratic forms",
  "authors": [
    "Lillian B. Pierce",
    "Damaris Schindler",
    "Melanie Matchett Wood"
  ],
  "comment": "66 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "It is classically known that the circle method produces an asymptotic for the number of representations of a tuple of integers $(n_1,\\ldots,n_R)$ by a system of quadratic forms $Q_1,\\ldots, Q_R$ in $k$ variables, as long as $k$ is sufficiently large; reducing the required number of variables remains a significant open problem. In this work, we consider the case of 3 forms and improve on the classical result by reducing the number of required variables to $k \\geq 10$ for \"almost all\" tuples, under appropriate nonsingularity assumptions on the forms $Q_1,Q_2,Q_3$. To accomplish this, we develop a three-dimensional analogue of Kloosterman's circle method, in particular capitalizing on geometric properties of appropriate systems of three quadratic forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-15T22:07:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic forms",
      "representations",
      "circle method produces",
      "appropriate nonsingularity assumptions",
      "kloostermans circle method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 66,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150904757P"
    }
  }
}