{"paper":{"title":"To the Hilbert class field from the hypergeometric modular function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Atsuhira Nagano, Hironori Shiga","submitted_at":"2015-11-10T00:11:26Z","abstract_excerpt":"In this article we make an explicit approach to the higher degree case of the problem: \" For a given $CM$ field $M$, construct its maximal abelian extension $C(M)$ (i.e. the Hilbert class field) by the adjunction of special values of certain modular functions\" in a restricted case. We make our argument based on Shimura's main result on the complex multiplication theory of his article in 1967. His main result is constructed for a quaternion algebra $B$ over a totally real number field $F$. We determine the modular function which gives the canonical model for the case $B$ is coming from an arith"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02941","kind":"arxiv","version":5},"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"}