Normal bases for rings of integers and modular units
Let \(K\) be an imaginary quadratic field with discriminant \(d_ K< -4\), \(d_ K\equiv 2,3\bmod 4\), and \(p\) a prime number, \(p\equiv 1\bmod 8\), \(p\) splits in \(K\). Furthermore, let \(\Omega_ p\) be the ring class field over \(K\) with conductor \(p\) and \(K(p)\) the ray class field over \(K\) with conductor \(p\). An explicit basis is constructed for the ring of integers of the unique quadratic extension of \(\Omega_ p\) contained in \(k(p)\) over the ring of integers of \(\Omega_ p\). This uses certain classical modular units considered by Deuring and Hecke.
scientific article; zbMATH DE number 617426
scientific article