论文标题
GCD和LCM-SUM的平均值估计值
Mean value estimates of gcd and lcm-sums
论文作者
论文摘要
我们平均研究广义GCD和LCM函数的分布。由$（m，n）_b $表示的广义GCD函数是最大的$ b $ th power除数，$ m $和$ n $。同样，由$ [m，n] _b $表示的广义LCM函数是最小的$ b $ th power多$ m $和$ n $的电源。我们为$（m，n）_b $的算术，几何和谐波均值的平均顺序得出渐近公式。此外，我们还推断出具有错误术语的渐近公式，用于$（n_1，n_2，\ cdots，n_k）_b $和$ [n_1，n_1，n_2，\ cdots，n_k] _b $在一组晶格上，从而将以前的某些工作概括为GCD和LCM-S-Sum-Sum-Sum-sum exteres。
We study the distribution of the generalized gcd and lcm functions on average. The generalized gcd function, denoted by $(m,n)_b$, is the largest $b$-th power divisor common to $m$ and $n$. Likewise, the generalized lcm function, denoted by $[m,n]_b$, is the smallest $b$-th power multiple common to $m$ and $n$. We derive asymptotic formulas for the average order of the arithmetic, geometric, and harmonic means of $(m,n)_b$. Additionally, we also deduce asymptotic formulas with error terms for the means of $(n_1,n_2,\cdots, n_k)_b$, and $[n_1,n_2,\cdots, n_k]_b$ over a set of lattice points, thereby generalizing some of the previous work on gcd and lcm-sum estimates.
