{
  "id": "1605.02478",
  "version": "v1",
  "published": "2016-05-09T08:54:14.000Z",
  "updated": "2016-05-09T08:54:14.000Z",
  "title": "Square-full polynomials in short intervals and in arithmetic progressions",
  "authors": [
    "Edva Roditty-Gershon"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the variance of sums of the indicator function of square-full polynomials in both arithmetic progressions and short intervals. Our work is in the context of the ring $F_{q}[T]$ of polynomials over a finite field $F_{q}$ of $q$ elements, in the limit $q\\rightarrow\\infty$. We use a recent equidistribution result due to N. Katz to express these variances in terms of triple matrix integrals over the unitary group, and evaluate them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-09T08:54:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "short intervals",
      "arithmetic progressions",
      "square-full polynomials",
      "triple matrix integrals",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}