The mean vcalue of the product of class numbers of paired quadratic fields I

Let $k$ be a number field and $\tilde k$ a fixed quadratic extension of $k$. In this paper and its companion, 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 $\tilde k$.