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

Theophilus Agama

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

Number Theory 2017-06-28 v1

Authors: Theophilus Agama

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 $E(f,g;x)=\# \{n\leq x:f(n)=g(n)\}$ . We establish a lower bound for $E(\Omega,g,x)$ .

Keywords

multiplicative function additive function prime factors with multiplicity lower bound proximity

Cite

@article{arxiv.1706.08646,
  title  = {On the proximity of multiplicative functions to the function counting prime factors with multiplicity},
  author = {Theophilus Agama},
  journal= {arXiv preprint arXiv:1706.08646},
  year   = {2017}
}

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