{"paper":{"title":"Analogues of Alladi's formula over global function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Biao Wang, Lian Duan, Shaoyun Yi","submitted_at":"2020-10-21T15:20:09Z","abstract_excerpt":"In this paper, we show an analogue of Kural, McDonald and Sah's result on Alladi's formula for global function fields. Explicitly, we show that for a global function field $K$, if a set $S$ of prime divisors has a natural density $\\delta(S)$ within prime divisors, then $$-\\lim_{n\\to\\infty} \\sum_{\\substack{1\\le \\deg D\\le n\\\\ D\\in \\mathfrak{D}(K,S)}}\\frac{\\mu(D)}{|D|}=\\delta(S),$$ where $\\mu(D)$ is the M\\\"{o}bius function on divisors and $\\mathfrak{D}(K,S)$ is the set of all effective distinguishable divisors whose smallest prime factors are in $S$. As applications, we get the analogue of Dawsey"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.11069","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/2010.11069/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"}