THE MEAN VALUE OF THE PRODUCT OF CLASS NUMBERS OF PAIRED QUADRATIC FIELDS I

Abstract

Let $k$ be a number field and $\tilde{k}$ 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 $F,F^*\not=\tilde{k}$ contained in the biquadratic extensions of $k$ containing $\tilde{k}$.