{"paper":{"title":"Distribution of irrational zeta values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"St\\'ephane Fischler (LM-Orsay)","submitted_at":"2013-10-07T06:18:51Z","abstract_excerpt":"In this paper we refine Ball-Rivoal's theorem by proving that for any odd integer $a$ sufficiently large in terms of $\\epsilon>0$, there exist $[ \\frac{(1-\\epsilon)\\log a}{1+\\log 2}]$ odd integers $s$ between 3 and $a$, with distance at least $a^{\\epsilon}$ from one another, at which Riemann zeta function takes $\\Q$-linearly independent values. As a consequence, if there are very few integers $s$ such that $\\zeta(s)$ is irrational, then they are rather evenly distributed. The proof involves series of hypergeometric type estimated by the saddle point method, and the generalization to vectors of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1685","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"}