{"paper":{"title":"The Landau function and the Riemann Hypothesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jean-Louis Nicolas, Marc Deleglise","submitted_at":"2019-07-17T17:50:03Z","abstract_excerpt":"The Landau function $g(n)$ is the maximal order of an element of the symmetric group of degree $n$; it is also the largest product of powers of primes whose sum is $\\le n$. The main result of this article is that the property \" For all $n > 0$ , $log g(n) < li^{-1} (n))$ \" (where $li^{-1}(n)$ denotes the inverse function of the logarithmic integral) is equivalent to the Riemann hypothesis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07664","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"}