On the proximity of multiplicative functions to the function counting prime factors with multiplicity

2017/06/27 by Agama, Theophilus
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.08646

Abstract

We examine how closely a multiplicative function resembles an additive function. Given a multiplicative function g and an additive function f, we examine the size of the quantity E(f,g;x)=# \n≤ x:f(n)=g(n)\. We establish a lower bound for E(Ω,g,x).

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