  In the first part of this paper, we derive explicit expressions of the
semi-group densities of generalized stochastic areas arising from the Anti-de
Sitter and the Hopf fibrations. Motivated by the number-theoretical connection
between the Heisenberg group and Dirichlet series, we express the Mellin
transform of the generalized stochastic area corresponding to the
one-dimensional Anti de Sitter fibration as a series of Riemann Zeta function
evaluated at integers. In the second part of the paper, we focus on winding
processes around the origin in the Poincar\'e disc and in the complex
projective line. More pricesely, we derive the fixed-time marginal density of
the former process while we give a ultraspherical series expansion of the
characteristic function of the latter.
