{"paper":{"title":"Ap\\'ery's theorem and problems for the values of Riemann's zeta function and their $q$-analogues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CA","math.CO"],"primary_cat":"math.NT","authors_text":"Wadim Zudilin","submitted_at":"2013-12-25T04:38:21Z","abstract_excerpt":"This monograph is intended to be considered as my habilitation (D.Sc.) thesis; because of that and as everything has already appeared in English, it is performed exclusively in Russian.\n  The monograph comprises a detailed introduction and seven chapters that represent part of my work influenced by Ap\\'ery's proof from 1978 of the irrationality of $\\zeta(2)$ and $\\zeta(3)$, the values of Riemann's zeta function. Chapter 1 is about \"at least one of the four numbers $\\zeta(5)$, $\\zeta(7)$, $\\zeta(9)$ and $\\zeta(11)$ is irrational\" (based in part on arXiv:math.NT/0206176). Chapter 2 explains a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6919","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"}