{"paper":{"title":"Formulas for Chebotarev densities of Galois extensions of number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Katharine Woo, Naomi Sweeting","submitted_at":"2018-07-04T19:04:46Z","abstract_excerpt":"We generalize the Chebotarev density formulas of Dawsey (2017) and Alladi (1977) to the setting of arbitrary finite Galois extensions of number fields $L/K$. In particular, if $C \\subset G = \\textrm{Gal}(L/K)$ is a conjugacy class, then we establish that the Chebotarev density is the following limit of partial sums of ideals of $K$: \\[ -\\lim_{X\\rightarrow\\infty} \\sum_{\\substack{2\\leq N(I)\\leq X \\\\ I \\in S(L/K; C)}} \\frac{\\mu_K(I)}{N(I)} = \\frac{|C|}{|G|}, \\] where $\\mu_K(I)$ denotes the generalized M\\\"obius function and $S(L/K;C)$ is the set of ideals $I\\subset \\mathcal{O}_K$ such that $I$ has"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01744","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":""},"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"}