A mean value theorem for the square of class number times regulator of   quadratic extensions
  Let $k$ 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. 
Takashi Taniguchi