Proof of class number formulae by machine (Q1297611)

Let \(p=4N^2+1\) be a prime number, \(\;K={\mathbb Q}(\sqrt{p})\;\) a real quadratic number field over the rationals \( {\mathbb Q}\) . Assuming the ideal class number of \( K \) is one, the authors give class number formulae in \(N\) for the imaginary quadratic fields \(\;{\mathbb Q}(\sqrt{-pq})\;\) with \(\;q=3,\;7,\;11,\;19,\;23,\;31,\;43\;\) and \(47\). This work is based on the second author's paper [ Chin. Sci. Bull. 36, 1145-1147 (1991; Zbl 0764.11044)], using a computer LEO386/25.