2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173782We give a geometric description of the motion of eigenvalues of a Brownian motion with values in some matrix spaces. In the second part we consider a paper by Polya where he introduced a function close to the Riemann zeta function, which satisfies Riemann hypothesis. We show that each of these two functions can be related to Brownian motion on a symmetric space.ProbabilityNumber TheoryRepresentation Theory60J65, 11M06text