{"paper":{"title":"A new formula for Chebotarev densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Madeline Locus Dawsey","submitted_at":"2017-03-23T18:16:23Z","abstract_excerpt":"We give a new formula for the Chebotarev densities of Frobenius elements in Galois groups. This formula is given in terms of smallest prime factors $p_{\\mathrm{min}}(n)$ of integers $n\\geq2$. More precisely, let $C$ be a conjugacy class of the Galois group of some finite Galois extension $K$ of $\\mathbb{Q}$. Then we prove that $$-\\lim_{X\\rightarrow\\infty}\\sum_{\\substack{2\\leq n\\leq X\\\\[1pt]\\left[\\frac{K/\\mathbb{Q}}{p_{\\mathrm{min}}(n)}\\right]=C}}\\frac{\\mu(n)}{n}=\\frac{\\#C}{\\#G}.$$ This theorem is a generalization of a result of Alladi from 1977 that asserts that largest prime divisors $p_{\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08194","kind":"arxiv","version":4},"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/1703.08194/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"}