Criteria of class number \(h(K) =1\) for real quadratic number fields (Q1210248)

The author is primarily concerned with class number one criteria for real quadratic fields \(\mathbb{Q}(\sqrt d)\) where \(d\) is of extended-Richaud-Degert (ERD) type; i.e., those \(d\) of the form \(d=s^ 2+r\) where \(r\mid 4s\). However, this problem was completely solved by \textit{R. A. Mollin} and \textit{H. C. Williams} in Number Theory, Proc. 1st Conf. Can. Number Theory Assoc., Banff 1988, 417-425 (1990; Zbl 0696.12004). The author's first result Theorem 1 on the zeta function is partially new (as he acknowledges).