关于两个新数论函数的 Dirichlet 级数

摘要

Two new arithmetical function U(n)andV(n)are defined ,and the convergent proper‐ties of the Dirichlet series ∑▌n= 1 (-1 )n Us (n) and ∑▌n= 1 (-1 )n V s (n) are studied .By using the elementary and analytic method ,the identities of Dirichlet series of two new arithmetic function is achieved , and two interesting mean value theorems are is obtained .The relevant research work of classi‐cal arithmetical function is developed .%定义两个新的算术函数U （n）及V （n），研究由U （n）及V （n）组成的一类Dirichlet级数的收敛性。利用初等方法和解析方法，给出两个新数论函数Dirichlet级数的恒等式，得到两个有趣的均值定理。从而拓展了经典算术函数的相关研究。