The mean value of the product of class numbers of paired quadratic fields. I

Abstract

Let $k$ be a number field and $\ti k$ a fixed quadratic extension of $k$. In this paper and its companions, we find the mean value of the product of class numbers and regulators of two quadratic extensions $F,F^*\not=\ti k$ contained in the biquadratic extensions of $k$ containing $\ti k$.