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A mean value theorem for the square of class number times regulator of quadratic extensions. (English) Zbl 1231.11111
Summary: Let \(k\) be a number field. In this paper, we give a formula for the mean value of the square of class number times regulator 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 pairs of quaternion algebras. We also prove an asymptotic formula of the correlation coefficient for class number times regulator of certain families of quadratic extensions.

MSC:
11M41 Other Dirichlet series and zeta functions
11S90 Prehomogeneous vector spaces
11S40 Zeta functions and \(L\)-functions
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References:
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