{
  "id": "2305.05071",
  "version": "v1",
  "published": "2023-05-08T22:20:09.000Z",
  "updated": "2023-05-08T22:20:09.000Z",
  "title": "Rational lines on diagonal hypersurfaces and subconvexity via the circle method",
  "authors": [
    "Trevor D. Wooley"
  ],
  "comment": "22 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Fix $k,s,n\\in \\mathbb N$, and consider non-zero integers $c_1,\\ldots ,c_s$, not all of the same sign. Provided that $s\\ge k(k+1)$, we establish a Hasse principle for the existence of lines having integral coordinates lying on the affine diagonal hypersurface defined by the equation $c_1x_1^k+\\ldots +c_sx_s^k=n$. This conclusion surmounts the conventional convexity barrier tantamount to the square-root cancellation limit for this problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-08T22:20:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45",
      "11D72",
      "11P55"
    ],
    "keywords": [
      "circle method",
      "rational lines",
      "subconvexity",
      "conventional convexity barrier tantamount",
      "square-root cancellation limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}