2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100917Let $k$ be a number field. In this paper, we give a formula for the mean value of the square of class numbers times regulators for certain families of quadratic extensions of $k$ characterized by finitely many local conditions. We approach this by using the theory of the zeta function associated with the space of pair of quaternion algebras.35 pages, AMS LaTeX; added a reference and rewrote Section 1Number Theory11M41text