%0 Journal Article
%T 一类数论函数的新进展<br>Further Research Progress on a Class of Arithmetic Functions
%A 陈亚菲
%A 尤利华   &lt
%A br&gt
%A CHEN Yafei
%A YOU Lihua
%J 华南师范大学学报（自然科学版）
%D 2018
%R 10.6054/j.jscnun.2017027
%X 进一步研究了满足条件 f(u2+kv2)=f2(u)+kf2(v)的数论函数 f(n),证明了其在k=6的情形下可分成3类,进而验证了关于f(n)的猜想在k=6时是正确的. 进一步地,总结了研究过程中出现的一些有趣结果,指出了该数论函数在参数k的不同取值下,其证明过程中出现的一些联系与区别,旨在为猜想的完全证明提供一些可能的理论支撑.<br>： The arithmetic function f(n) which satisfies f(u2+kv2)=f2(u)+kf2(v) is further studied. It is proved that f(n) can be divided into three classes with k=6, and thus the conjecture of f(n) in the case of k=6 is verified. What’s more,some interesting results are presented. Some relations and distinction in the process of the proof with different values of parameter k are pointed out, which aims at providing some possible theoretical support for the complete proof of the conjecture
%K 数论函数
%K 函数方程
%K 刻画
%K &lt
%K br&gt
%K arithmetic function
%K functional equation
%K charaterization
%U http://journal.scnu.edu.cn:8080/jwk_xbzrb/CN/abstract/abstract4471.shtml