{"paper":{"title":"Sharpenings of Li's criterion for the Riemann Hypothesis","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NT","authors_text":"Andr\\'e Voros","submitted_at":"2005-06-16T11:17:55Z","abstract_excerpt":"Exact and asymptotic formulae are displayed for the coefficients $\\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \\to \\infty$ we obtain that if (and only if) the Hypothesis is true, $\\lambda_n \\sim n(A \\log n +B)$ (with $A>0$ and $B$ explicitly given, also for the case of more general zeta or $L$-functions); whereas in the opposite case, $\\lambda_n$ has a non-tempered oscillatory form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506326","kind":"arxiv","version":2},"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"}