论文标题
涉及功能$ω（N）$和LCM功能的双曲线总和
Hyperbolic summation involving the function $Ω(n)$ and lcm
论文作者
论文摘要
我们研究总和$ \ sum_ {abc \ leq x}ω（[[a，b，c]）$，其中$ω（n）$表示$ n \ in \ mathbb {z} _ {z} _ {\ geq 1} $的$ n \ in $ n \的独特质量分隔线的数量，与乘以$（$ c），b，b，b，b，c c. $ [a，b，c] = \ operatorName {lcm}（a，b，c）$。该总和在双曲线区域$ \ {（a，b，c）\ in \ mathbb {z} _ {\ geq 1}^3：abc \ leq x \} $上。
We study the sum $\sum_{abc \leq x} Ω([a,b,c])$, where $Ω(n)$ denotes the number of distinct prime divisors of $n \in \mathbb{Z}_{\geq 1}$, counted with multiplicity, and where $(a,b,c) = \gcd(a,b,c)$ and $[a,b,c] = \operatorname{lcm}(a,b,c)$. An asymptotic formula is derived for this sum over the hyperbolic region $\{(a,b,c) \in \mathbb{Z}_{\geq 1}^3 : abc \leq x\}$.
