论文标题
集合中主要因素的联合泊松分布
Joint Poisson distribution of prime factors in sets
论文作者
论文摘要
给定的脱节子集$ t_1，\ ldots，t_m $“不大”的数量最高为$ x $，我们为随机的整数$ n $从$ [1，x] $，$ m $维矢量列出$ n $ n $的质量因子数量从$ t_1，$ t_1，\ ldots $ po po cons o cors cons to cons frove cons contection，$ m $ n $ n $ n ulders cons of cons frove cons of cons from $ n $。我们使用主要因素的Kubilius模型给出了特定的收敛速率。当$ t_1，\ ldots，t_m $不受限制时，我们还显示了泊松类型的通用上限，并将其应用于一组$ t $的质量因素数量的分布，因为$ n $ $ n $具有$ k $ $ k $总质量因素。
Given disjoint subsets $T_1,\ldots,T_m$ of "not too large" primes up to $x$, we establish that for a random integer $n$ drawn from $[1,x]$, the $m$-dimensional vector enumerating the number of prime factors of $n$ from $T_1,\ldots,T_m$ converges to a vector of $m$ independent Poisson random variables. We give a specific rate of convergence using the Kubilius model of prime factors. We also show a universal upper bound of Poisson type when $T_1,\ldots,T_m$ are unrestricted, and apply this to the distribution of the number of prime factors from a set $T$ given that $n$ has $k$ total prime factors.
