{"paper":{"title":"Congruences arising from Ap\\'ery-type series for zeta values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood","submitted_at":"2011-08-09T09:54:52Z","abstract_excerpt":"Recently, R. Tauraso established finite $p$-analogues of famous Ap\\'ery series for $\\zeta(2)$ and $\\zeta(3).$ In this paper, we present several congruences for finite central binomial sums arising from the truncation of Ap\\'ery-type series for $\\zeta(4)$ and $\\zeta(5).$ We also prove a $p$-analogue of Zeilberger's series for $\\zeta(2)$ confirming a conjecture of Z. W. Sun."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1893","kind":"arxiv","version":3},"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"}