Riemann Zeta Function and Functional Equation IX

Japanese version
Perhaps, One of the oldest approach is the Mertens conjecture. In 1885 Mr. Stieltjes propose the conjecture. But now it is thought that the Mertens conjecture might be wrong. However, this approach relate Brownian movement with Riemann zeta and it is thought to be very important and fundamental.

Riemann zeta function and Functional Equation (IX)

I described in this article that the Mertens conjecture is important and Erdos-Kac limit formula relates statistic dynamics with Riemann zeta function.