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

Takashi Taniguchi

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

Number Theory 2007-05-23 v3

Authors: Takashi Taniguchi

Abstract

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.

Keywords

mean value theorem class number regulator quadratic extensions number field zeta function quaternion algebras

Cite

@article{arxiv.math/0410531,
  title  = {A mean value theorem for the square of class number times regulator of quadratic extensions},
  author = {Takashi Taniguchi},
  journal= {arXiv preprint arXiv:math/0410531},
  year   = {2007}
}

Comments

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

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