四川大学学报（自然科学版）2021，Vol.58Issue(1)：1-6,6.DOI:10.19907/j.0490-6756.2021.011001
关于Jordan函数的gcd和函数的渐近估计
An asymptotic formula for the gcd-sum function of Jordan's totient function
摘要
Abstract
Let gcd(k ,j ) denote the greatest common divisor of the positive integers k and j , r be any fixed positive integer .Let Mr ( x;f )为Mr (x;f )= ∑k≤ x 1/kr+1 k∑j= 1 jr f (gcd(k ,j)) ,where x ≥2 is any large real num-ber and f is any arithmetical function .Let Jk denote Jordan's totient function defined for any integer n≥1by Jk (n)= nk ∏p|n(1 - 1/pk ).In this paper,by using the identity of Kiuchi on Mr(x;f)together with some analytic techniques ,we present an asymptotic formula of Mr(x;Jk) .These complement and strengthen the corresponding results obtained by Kiuchi and Saadeddin in 2018 .关键词
GCD和函数/若当函数/均值/部分和/黎曼Zeta函数Key words
Gcd-sum function/Jordan's totient function/Mean value/Partial summation/Riemann Zeta-function分类
数理科学引用本文复制引用
李林峰,谭千蓉,陈龙..关于Jordan函数的gcd和函数的渐近估计[J].四川大学学报（自然科学版）,2021,58(1):1-6,6.基金项目
国家自然科学基金(11771304) （11771304）
攀枝花学院博士基金 （）
