{"paper":{"title":"Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","submitted_at":"2009-06-11T15:13:10Z","abstract_excerpt":"We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\\sum\\limits_{\\substack{p\\leq x p\\equiv a \\bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\\sum_{p\\equiv a \\bmod{q}} (\\log(1-1/p)+1/p)$, for $q \\in \\{3$, ..., $100\\}$ and $(q, a) = 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2132","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"}