{"paper":{"title":"The Nicolas and Robin inequalities with sums of two squares","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. Wesley Nevans, Derrick N. Hart, Pieter Moree, William D. Banks","submitted_at":"2007-10-12T10:20:01Z","abstract_excerpt":"In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality $\\sigma(n)<e^\\gamma n\\log\\log n$ holds for every integer $n>5040$, where $\\sigma(n)$ is the sum of divisors function, and $\\gamma$ is the Euler-Mascheroni constant. We exhibit a broad class of subsets $\\cS$ of the natural numbers such that the Robin inequality holds for all but finitely many $n\\in\\cS$. As a special case, we determine the finitely many numbers of the form $n=a^2+b^2$ that do not satisfy the Robin inequality. In fact, we prove our assertions with the Nicolas inequality $n/\\phi(n)<e^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2424","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"}