{"paper":{"title":"Irrationality of $\\zeta_q(1)$ and $\\zeta_q(2)$","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Kelly Postelmans, Walter Van Assche","submitted_at":"2006-04-13T14:04:02Z","abstract_excerpt":"In this paper we show how one can obtain simultaneous rational approximants for $\\zeta_q(1)$ and $\\zeta_q(2)$ with a common denominator by means of Hermite-Pade approximation using multiple little q-Jacobi polynomials and we show that properties of these rational approximants prove that 1, $\\zeta_q(1)$, $\\zeta_q(2)$ are linearly independent over the rationals. In particular this implies that $\\zeta_q(1)$ and $\\zeta_q(2)$ are irrational. Furthermore we give an upper bound for the measure of irrationality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604312","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"}