{"paper":{"title":"Five families of rapidly convergent evaluations of zeta values","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.NT","authors_text":"David Broadhurst","submitted_at":"2024-01-17T06:21:22Z","abstract_excerpt":"This work derives 5 methods to evaluate families of odd zeta values by combining a power of $\\pi$ with Lambert series whose ratios of successive terms tend to $e^{-\\pi\\sqrt{a}}$ with integers $a\\ge7$, outperforming Ramanujan's results with merit $a=4$. Families with $a=7$ and $a=8$ evaluate $\\zeta(2n+1)$. Families with $a=9$ and $a=16$ evaluate $\\zeta(4n+1)$ with faster convergence. A fifth family with $a=12$ evaluates $\\zeta(6n+1)$ and gives the fastest convergence for $\\zeta(6n+7)$. Members of three of the families were discovered empirically by Simon Plouffe. An intensive new search strongl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.08997","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/2401.08997/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"}