{"paper":{"title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Archisman Bhattacharjee","submitted_at":"2026-07-15T20:21:59Z","abstract_excerpt":"For $a,b,c \\in \\mathbb{Q}$, the exceptional set associated to the Gauss hypergeometric function $_2F_1(a,b,c;z)$ is defined by $E(a,b,c) := \\{ z \\in \\overline{\\Q} \\mid {}_2F_1(a,b,c;z) \\in \\overline{\\mathbb{Q}} \\}.$ In this paper, the exceptional sets $E(a,b,c)$ are determined explicitly for each $_2F_1(a,b,c;z)$ whose monodromy group is an arithmetic triangle group in Takeuchi's class I. The description is obtained via hypergeometric--modular identities together with transcendence results for periods of abelian varieties due to W\\\"ustholz, and classical result of Schneider on algebraic values"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16331","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16331/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"}