{"paper":{"title":"The Strong Chowla-Milnor spaces and a conjecture of Gun, Murty and Rath","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tapas Chatterjee","submitted_at":"2013-08-29T12:29:50Z","abstract_excerpt":"In a recent work, Gun, Murty and Rath formulated the Strong Chowla-Milnor conjecture and defined the Strong Chowla-Milnor space. In this paper, we prove a non-trivial lower bound for the dimension of these spaces. We also obtain a conditional improvement of this lower bound and noted that an unconditional improvement of this lower bound will lead to irrationality of both $\\zeta(k)$ and $\\zeta(k)/ \\pi^k$ for all odd positive integers $k>1$. Following Gun, Murty and Rath, we define generalized Zagier spaces $V_p(K)$ for multiple zeta values over a number field $K$. We prove that the dimension of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6448","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"}