A mean value theorem for the square of class number times regulator of quadratic extensions

Details A mean value theorem for the square of class number times regulator of quadratic extensions A mean value theorem for the square of class number times regulator of quadratic extensions

2004-10-25

arxiv.org/abs/math/0410531v3

Mathematics

Number Theory

35 pages, AMS LaTeX; added a reference and rewrote Section 1

Scientific paper

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.

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