{
  "annotation_id": "61f04481-8b7d-4143-a58c-9c64df2168b7",
  "date_created": "2026-02-17T05:53:26.424000Z",
  "date_modified": "2026-02-17T05:53:26.424000Z",
  "file_hash": "733eb406ade7cca84a345930ecd587004f423ce92be3a9eb2ba02513dff4f13a",
  "private": false,
  "record": {
    "abstract": "In this paper, I utilize a variant of the Selberg--Delange method to find quantitative estimates of the sums \\[M_{k,\\omega}(x,y)=\\sum_{\\substack{p_{1}(n)\u003e y\\\\ n\\leq x} } \\mu(n) {\\omega(n)-1\\choose k-1},\\] where $y$ can grow with $x$ but we must have $y\\leq Y_0\\exp(\\mathscr{p}\\frac{\\log x}{(\\log\\log (x+1))^{1+\\epsilon}})$ with $Y_0,\\mathscr{p},\\epsilon\u003e0$. Moreover, I give preliminary upper bounds for the general range $1.9\\leq y\\leq x^{\\frac{1}{k}}$. In addition, I formalize the notions of subradical and radical dominance and discuss their relevance to the analytic approach of the study of arithmetic functions. Lastly, I give a fascinating formula related to the derivatives of the gamma function and the Hankel contour, which should be relevant for those employing the Selberg--Delange method to obtain higher-order terms.",
    "arxiv_id": "2601.10636",
    "authors": [
      "Yazan Alamoudi"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On subradically sifted sums related to Alladi\u0027s higher order duality between prime factors",
    "url": "https://arxiv.org/abs/2601.10636",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d1b79065-1cc6-4957-902b-f114b1d16217",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}