{
  "abstract": "Zero correlations offer a way to test the cuspidal structure of an automorphic L-function, but their leading self statistics retain only coarse degree and multiplicity data. We therefore adjoin a specified cuspidal L-function as a probe and study the resulting raw mixed correlations. Assuming a factorization into cuspidal L-functions over Q, we show that a mixed pair statistic detects the probe's occurrence and recovers its multiplicity. A suitable Gevrey-order-two test eliminates the smooth-density terms and gives a subexponential error. For arbitrary smooth plateau tests, the prime number theorem of Harcos and Thorner gives an error smaller than every fixed inverse power of log T, without a self-contragredience assumption. The stronger prime number theorem of Liu and Ye gives a subexponential remainder under its stated structural assumptions, with the possible norm-twist terms made explicit. To obtain arithmetic information beyond this overlap, we compute the correlation expansion at every fixed level and inverse-logarithmic order within the original strict small-support range. We treat the pair and higher correlations separately, using Jiang's rational-field fixed-data estimates to justify the required prime-power convergence. The pair calculation identifies the mixed arithmetic finite parts and gives detailed error estimates, including the contribution of norm twists. The higher-level calculation retains connected prime-power invariants, whose first cubic contribution appears at order (log T)^{-3}. Explicit third- and fourth-level formulas and examples explain the arithmetic content of these coefficients and the limitations of self-correlations. Varying powers of the probe separates their mixed components. These formulas, together with the distinct-index sieve, provide a collection of arithmetic probe responses toward the further problem of recovering automorphic induction structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02058",
  "author_total": 1,
  "authors": [
    {
      "name": "Yangbo Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0zwf73ncrkmys.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02058",
  "fulltext_url": null,
  "id": "0zwf73ncrkmys",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02058",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02058",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0zwf73ncrkmys.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02058",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02058"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Probing automorphic induction through zero correlations and secondary arithmetic terms",
  "title_text": "Probing automorphic induction through zero correlations and secondary arithmetic terms",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0zwf73ncrkmys",
  "venue": "arXiv",
  "versions": []
}