{"paper":{"title":"Time- and Space-Efficient Evaluation of Some Hypergeometric Constants","license":"","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Emmanuel Thom\\'e (INRIA Lorraine - LORIA), Eugene Zima, Guillaume Hanrot (INRIA Lorraine - LORIA), Howard Cheng, Paul Zimmermann (INRIA Lorraine - LORIA)","submitted_at":"2007-01-25T08:07:38Z","abstract_excerpt":"The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \\log^2 d)$ and space complexity of $O(d \\log d)$ or $O(d)$. Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm with the same asymptotic complexity, but more efficient in practice. Our implementation of this algorithm improves slightly over existing programs for the computation of $\\pi$, and we announce a new record of 2 billion digits for $\\zeta(3)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0701151","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":""},"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"}