{"paper":{"title":"On correlation of the 3-fold divisor function with itself","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David T. Nguyen","submitted_at":"2022-06-13T02:12:17Z","abstract_excerpt":"Let $\\zeta^k(s) = \\sum_{n=1}^\\infty \\tau_k(n) n^{-s}, \\Re s > 1$.\n  We present three conditional results on the ternary additive correlation sum $$\\sum_{n\\le X} \\tau_3(n) \\tau_3(n+h),\\quad (h\\ge 1),$$ and give numerical verifications of our method. The first is a conditional proof for the full main term of the above correlation sum for any composite shift $1 \\le h \\le X^{2/3}$, on assuming an averaged level of distribution for the three-fold divisor function $\\tau_3(n)$ in arithmetic progressions to level two-thirds. The second is a conditional derivation for the leading order main term asympt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.05877","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.05877/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}