{"paper":{"title":"Chebyshev Upper Estimates for Beurling's Generalized Prime Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jasson Vindas","submitted_at":"2012-05-18T23:38:40Z","abstract_excerpt":"Let $N$ be the counting function of a Beurling generalized number system and let $\\pi$ be the counting function of its primes. We show that the $L^{1}$-condition $$ \\int_{1}^{\\infty}|\\frac{N(x)-ax}{x}|\\frac{\\mathrm{d}x}{x}<\\infty $$ and the asymptotic behavior $$N(x)=ax+O(\\frac{x}{\\log x}),$$ for some $a>0$, suffice for a Chebyshev upper estimate $$ \\frac{\\pi(x)\\log x}{x}\\leq B<\\infty. $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4281","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"}