{
  "id": "2306.09102",
  "version": "v1",
  "published": "2023-06-15T12:55:00.000Z",
  "updated": "2023-06-15T12:55:00.000Z",
  "title": "The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function",
  "authors": [
    "Keith Billington",
    "Maddie Cheng",
    "Jordan Schettler",
    "Ade Irma Suriajaya"
  ],
  "comment": "22 pages (content in 20 pages), a student project conducted at SJSU under Kyushu University SENTAN-Q",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we prove an unconditional form of Fujii's formula for the average number of Goldbach representations and show that the error in this formula is determined by a general zero-free region of the Riemann zeta-function, and vice versa. In particular, we describe the error in the unconditional formula in terms of the remainder in the Prime Number Theorem which connects the error to zero-free regions of the Riemann zeta-function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-15T12:55:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P32",
      "11N05",
      "11N37",
      "11M26"
    ],
    "keywords": [
      "riemann zeta-function",
      "average number",
      "goldbach representations",
      "prime number theorem",
      "general zero-free region"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}