{"paper":{"title":"Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Leonid G. Fel","submitted_at":"2011-08-03T22:59:07Z","abstract_excerpt":"We consider a wide class of summatory functions F{f;N,p^m}=\\sum_{k\\leq N}f(p^m k), m\\in \\mathbb Z_+\\cup {0}, associated with the multiplicative arithmetic functions f of a scaled variable k\\in \\mathbb Z_+, where p is a prime number. Assuming an asymptotic behavior of summatory function, F{f;N,1}\\stackrel{N\\to \\infty}{=}G_1(N) [1+ {\\cal O}(G_2(N))], where G_1(N)=N^{a_1}(log N)^{b_1}, G_2(N)=N^{-a_2}(log N)^{-b_2} and a_1, a_2\\geq 0, -\\infty < b_1, b_2< \\infty, we calculate a renormalization function defined as a ratio, R(f;N,p^m)=F{f;N,p^m}/F{f;N,1}, and find its asymptotics R_{\\infty}(f;p^m) w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0957","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"}