{"paper":{"title":"On discriminants of minimal polynomials of the Ramanujan $t_n$ class invariants","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sarth Chavan","submitted_at":"2022-10-03T02:00:05Z","abstract_excerpt":"We study the discriminants of the minimal polynomials $\\mathcal{P}_n$ of the Ramanujan $t_n$ class invariants, which are defined for positive integers $n\\equiv11\\pmod{24}$. The historical precedent for doing so comes from Gross and Zagier, which is known for computing the prime factorizations of certain resultants and discriminants of the Hilbert class polynomials $H_n$. We show that $\\Delta\\left(\\mathcal{P}_n\\right)$ divides $\\Delta\\left(H_n\\right)$ with quotient a perfect square, and as a consequence, we explicitly determine the sign of $\\Delta\\left(\\mathcal{P}_n\\right)$ based on the class g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.00681","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/2210.00681/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"}