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

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

2009-07-06

arxiv.org/abs/0907.0916v1

Mathematics

Number Theory

8 pages

Scientific paper

We compute the "moments" and its continuous anaougue of the random variable
$\N^r \ni (k_1, k_2, ..., k_r) \mapsto \gcd(n,k_1k_2... k_r) \in \N$ by a
purely elementary method. This generalizes a result of Kurokawa-Ochiai, which
computed its "average" using some analysis involving L-function.

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