I learned from Gian-Carlo Rota the following probabilistic motivation for looking at the Riemann zeta function: "subject to technical assumptions," the only probability measures on $\mathbb{N}$ for which the events of being divisible by distinct primes are independent are the ones which assign to a positive integer $n$ the probability $\frac{1}{n^s \zeta(s)}$ for some $s$.

I learned from Gian-Carlo Rota (Combinatorial snapshots) the following probabilistic motivation for looking at the Riemann zeta function: "subject to technical assumptions," the only probability measures on $\mathbb{N}$ for which the events of being divisible by distinct primes are independent are the ones which assign to a positive integer $n$ the probability $\frac{1}{n^s \zeta(s)}$ for some $s$.

I learned from Gian-Carlo Rota the following probabilistic motivation for looking at the Riemann zeta function: "subject to technical assumptions," the only probability measures on $\mathbb{N}$ for which the events of being divisible by distinct primes are independent are the ones which assign to a positive integer $n$ the probability $\frac{1}{n^s \zeta(s)}$ for some $s$.

I learned from Gian-Carlo Rota the following probabilistic motivation for looking at the Riemann zeta function: "subject to technical assumptions," the only probability measures on $\mathbb{N}$ for which the events of being divisible by distinct primes are independent are the ones which assign to a positive integer $n$ the probability $\frac{1}{n^s \zeta(s)}$ for some $s$.