A function f ： N → Ris called additive if f（mn） = f（m） ＋f （n） for all m, n with （m, n） = 1. Let μ（x） = maxn≤x（f（n） - f（n ＋ 1）） and v（x） = maxn≤x（f（n ＋ 1） - f（n））. In 1979, Ruzsa proved ...A function f ： N → Ris called additive if f（mn） = f（m） ＋f （n） for all m, n with （m, n） = 1. Let μ（x） = maxn≤x（f（n） - f（n ＋ 1）） and v（x） = maxn≤x（f（n ＋ 1） - f（n））. In 1979, Ruzsa proved that there exists a constant c such that for any additive function f, μ（x） ≤ cv（x^2） ＋ cf, where cf is a constant depending only on f. Denote by Raf the least such constant c. We cMl Raf Ruzsa＇s constant on additive functions. In this paper, we prove that Raf≤ 20.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11071121and11126302)supported by Natural Science Foundation of the Jiangsu Higher Education Institutions(GrantNo.11KJB110006) the Foundation of Nanjing University of Information Science&Technology(Grant No.20110421)
文摘A function f ： N → Ris called additive if f（mn） = f（m） ＋f （n） for all m, n with （m, n） = 1. Let μ（x） = maxn≤x（f（n） - f（n ＋ 1）） and v（x） = maxn≤x（f（n ＋ 1） - f（n））. In 1979, Ruzsa proved that there exists a constant c such that for any additive function f, μ（x） ≤ cv（x^2） ＋ cf, where cf is a constant depending only on f. Denote by Raf the least such constant c. We cMl Raf Ruzsa＇s constant on additive functions. In this paper, we prove that Raf≤ 20.
