On the smallest discriminants of quaternionic fields
Let \(G\) be the quaternion group of order \(4n\), and let \(N\) be a normal extension of the field \(\mathbb{Q}\) of rational numbers with Galois group isomorphic to \(G\). This paper deals with the discriminants of \(N\), particularly when \(n\) is a prime number. We find the smallest discriminants (real and imaginary) when \(n= 2, 3\) or 5. In addition we determine also all fields \(N\) with \(d_N\leq 10^{16}\) if \(n=2\) and all fields \(N\) with \(d_N\leq 10^{20}\) if \(n=3\).
scientific article; zbMATH DE number 938582