On the random variable $\N^r \ni (k_1, k_2, ..., k_r) \mapsto \gcd(n,k_1k_2... k_r) \in \N$

Norihiko Minami

paper

On the random variable $N^{r} ∋ (k_{1}, k_{2}, ..., k_{r}) \mapsto g cd (n, k_{1} k_{2} ... k_{r}) \in N$

arXiv:0907.0916

Abstract

We compute the "moments" and its continuous anaougue of the random variable $N^{r} ∋ (k_{1}, k_{2}, ..., k_{r}) \mapsto g cd (n, k_{1} k_{2} ... k_{r}) \in N$ by a purely elementary method. This generalizes a result of Kurokawa-Ochiai, which computed its "average" using some analysis involving L-function.

8 pages

On the random variable Nr∋(k1​,k2​,...,kr​)↦gcd(n,k1​k2​...kr​)∈N

Abstract

On the random variable $N^{r} ∋ (k_{1}, k_{2}, ..., k_{r}) \mapsto g cd (n, k_{1} k_{2} ... k_{r}) \in N$