{"paper":{"title":"On Chudnovsky-Ramanujan Type Formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gleb Glebov, Imin Chen","submitted_at":"2016-09-08T21:11:59Z","abstract_excerpt":"In a well-known 1914 paper, Ramanujan gave a number of rapidly converging series for $1/\\pi$ which are derived using modular functions of higher level. D. V. and G. V. Chudnovsky in their 1988 paper derived an analogous series representing $1/\\pi$ using the modular function $J$ of level 1, which results in highly convergent series for $1/\\pi$, often used in practice. In this paper, we explain the Chudnovsky method in the context of elliptic curves, modular curves, and the Picard-Fuchs differential equation. In doing so, we also generalize their method to produce formulae which are valid around"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05778","kind":"arxiv","version":2},"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"}