{"paper":{"title":"On error term estimates \\`a la Walfisz for mean values of arithmetic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yuta Suzuki","submitted_at":"2018-11-06T18:57:00Z","abstract_excerpt":"Walfisz (1963) proved the asymptotic formula \\[ \\sum_{n\\le x}\\varphi(n) = \\frac{3}{\\pi^2}x^2+O(x(\\log x)^{\\frac{2}{3}}(\\log\\log x)^{\\frac{4}{3}}), \\] which improved the error term estimate of Mertens (1874) and had been the best possible estimate for more than 50 years. Recently, H.-Q. Liu (2016) improved Walfisz's error term estimate to \\[ \\sum_{n\\le x}\\varphi(n) = \\frac{3}{\\pi^2}x^2+O(x(\\log x)^{\\frac{2}{3}}(\\log\\log x)^{\\frac{1}{3}}). \\] We generalize Liu's result to a certain class of arithmetic functions and improve the result of Balakrishnan and P\\'etermann (1996). To this end, we provid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02556","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"}