{"paper":{"title":"Continued Fractions and Irrationality Measures for Chowla--Selberg Gamma Quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Henri Cohen, Wadim Zudilin","submitted_at":"2025-09-30T19:45:28Z","abstract_excerpt":"We give 39 rapidly convergent continued fractions for Chowla--Selberg gamma quotients, and deduce good irrationality measures for 20 of them, including for $\\operatorname{CS}(-3)=(\\Gamma(1/3)/\\Gamma(2/3))^3$, for $a^{1/4}\\operatorname{CS}(-4)=a^{1/4}(\\Gamma(1/4)/\\Gamma(3/4))^2$ with $a=12$ and $a=1/5$, and for $\\operatorname{CS}(-7)=\\Gamma(1/7)\\Gamma(2/7)\\Gamma(4/7)/(\\Gamma(3/7)\\Gamma(5/7)\\Gamma(6/7))$. These appear to be the first proved and reasonable irrationality measures for gamma quotients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.00215","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/2510.00215/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"}