{
  "id": "1511.06824",
  "version": "v1",
  "published": "2015-11-21T03:40:32.000Z",
  "updated": "2015-11-21T03:40:32.000Z",
  "title": "Zero-density estimates for Epstein zeta function",
  "authors": [
    "Steven Gonek",
    "Yoonbok Lee"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the zeros of Epstein zeta functions associated with a positive definite quadratic form with rational coefficients in the vertical strip $ \\sigma_1 < \\Re s < \\sigma_2 $, where $ 1/2 < \\sigma_1 < \\sigma_2 < 1 $. When the class number of the quadratic form is bigger than 1, Voronin gives a lower bound and Lee gives an asymptotic formula for the number of zeros. In this paper, we improve their results by providing a new upper bound for the error term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-21T03:40:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "epstein zeta function",
      "zero-density estimates",
      "positive definite quadratic form",
      "class number",
      "rational coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151106824G"
    }
  }
}