有限域多项式环上的GCD和函数与LCM和函数的均值
The Means of Gcd-Sum Function and Lcm-Sum Function in the Ring on the Finite Filed
DOI: 10.12677/PM.2020.102010, PDF,    科研立项经费支持
作者: 李 欣：青岛大学，数学与统计学院，山东 青岛
关键词: 可乘函数；Dirichlet级数；黎曼Zeta函数；Dirichlet卷积；Multiplicative Function； Dirichlet Series； Riemann Zeta Function； Dirichlet Convolution
摘要: 最大公约数和最小公倍数问题是数论的经典问题之一，本文利用其和函数的可乘性和Dirichlet级数，研究Gcd和函数与Lcm和函数在有限域的多项式环上的均值并且与整数环上的结果对比得到一致结论。
Abstract: The greatest common divisor and the least common multiple are one of the classical problems in number theory. In this paper, we use the multiplicative function property and Dirichlet series to study the mean values of Gcd-sum function and Lcm-sum function on polynomial rings in finite fields. In the end, we compare with the results on integer rings and obtain consistent conclusions.
文章引用：李欣. 有限域多项式环上的GCD和函数与LCM和函数的均值[J]. 理论数学, 2020, 10(2): 55-64. https://doi.org/10.12677/PM.2020.102010

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