Brownian motion and Riemann zeta function

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In mathematics, the Brownian motion and the Riemann zeta function are two central objects of study originating from different fields - probability theory and analytic number theory - that have deep mathematical connections between them. The relationships between stochastic processes derived from the Brownian motion and the Riemann zeta function show in a sense inuitively the stochastic behaviour underlying the Riemann zeta function. A representation of the Riemann zeta function in terms of stochastic processes is called a stochastic representation.