有限域多项式环上广义gcd和函数的均值
The Mean Value of the Generalized gcd-Sum Function on the Polynomial Ring over Finite Field
摘要:
算术函数的均值问题是数论中的重要问题之一，尤其是与gcd函数有关的均值问题。本文在已知整数环上广义gcd和函数的均值的基础上，通过类比，讨论有限域多项式环上相应的广义gcd和函数的均值。
Abstract:
The mean value of arithmetic functions is one of the most important problems in number theory, especially the mean value of the gcd function. In this paper, the mean values of the corresponding generalized gcd-sum function on polynomial rings over finite fields are discussed by analogy on the basis of given mean values of the generalized gcd-sum function over integer ring.
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