English

A characterization of arithmetic functions satisfying $f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)$

Number Theory 2016-06-17 v1

Abstract

In this paper, we mainly discuss the characterization of a class of arithmetic functions f:NCf: N \rightarrow C such that f(u2+kv2)=f2(u)+kf2(v)f(u^{2}+kv^2)=f^{2}(u)+kf^{2}(v) (k,u,vN)(k, u, v \in N). We obtain a characterization with given condition, propose a conjecture and show the result holds for k{2,3,4,5}k \in \{2, 3, 4, 5 \}.

Keywords

Cite

@article{arxiv.1606.05039,
  title  = {A characterization of arithmetic functions satisfying $f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)$},
  author = {Lihua You and Yafei Chen and Pingzhi Yuan},
  journal= {arXiv preprint arXiv:1606.05039},
  year   = {2016}
}