{"paper":{"title":"Weak Inhomogeneous Poissonian Pair Correlation and Equidistribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Qing-Long Zhou, Zhiqin Tang","submitted_at":"2026-07-12T14:03:33Z","abstract_excerpt":"This paper investigates inhomogeneous Poissonian pair correlation (PPC), its weak form, and equidistribution. We establish that weak inhomogeneous PPC does not imply inhomogeneous PPC. Furthermore, we construct a sequence satisfying weak inhomogeneous PPC that fails to be equidistributed, which stands in sharp contrast to the homogeneous case. Finally, we prove that for distinct $\\gamma_1, \\gamma_2 \\in (0, \\frac{1}{2}]$, weak $\\gamma_1$-PPC does not imply weak $\\gamma_2$-PPC, showing that different inhomogeneous parameters give rise to mutually independent notions of weak inhomogeneous PPC."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10773","kind":"arxiv","version":1},"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/2607.10773/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"}