{
  "id": "2408.02776",
  "version": "v1",
  "published": "2024-08-05T18:55:00.000Z",
  "updated": "2024-08-05T18:55:00.000Z",
  "title": "Oscillatory integrals with phases arising from algebraic number fields",
  "authors": [
    "Robert Fraser"
  ],
  "comment": "40 Pages",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "We develop a theory of oscillatory integrals whose phase is given by the trace of a polynomial over an algebraic number field. We present an application to the singular integral for a version of Tarry's problem for algebraic integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-05T18:55:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B99"
    ],
    "keywords": [
      "algebraic number field",
      "oscillatory integrals",
      "phases arising",
      "singular integral",
      "tarrys problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}