{"paper":{"title":"The distribution of $G$-Weyl CM fields and the Colmez conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Adrian Barquero-Sanchez, Frank Thorne, Riad Masri","submitted_at":"2017-07-31T19:29:32Z","abstract_excerpt":"Let $G$ be a transitive subgroup of $S_d$ and $E$ be a CM field of degree $2d$ with a maximal totally real $G$-field. If the Galois group of the Galois closure of $E$ is isomorphic to the wreath product of $C_2$ and $G$, then we say that $E$ is a $G$-Weyl CM field.\n  Let $N_{2d}^{\\textrm{Weyl}}(X,G)$ count the $G$-Weyl CM fields $E$ of degree $2d$ with discriminant $|d_E| \\leq X$ and define \\begin{align*} N_{2d}^{\\textrm{Weyl}}(X):=\\sum_{G \\leq S_d}N_{2d}^{\\textrm{Weyl}}(X,G). \\end{align*} Further, let $N_{2d}^{\\textrm{cm}}(X)$ count the CM fields $E$ of degree $2d$ with discriminant $|d_E| \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00044","kind":"arxiv","version":3},"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"}