A problem on quadratic fields
For a quadratic field \(k\), let \(M_ k\) denote the Minkowski constant and \(\chi_ k\) the Kronecker character of \(k\). The author considers explicit determination of the sets \(K^ 0\), \(K^{-}\) and \(K^{+}\) consisting of those \(k\) for which all rational primes \(p\leq M_ k\) satisfy \(\chi_ k(p)=0, -1\) or \(+1\), respectively. He determines \(K^ 0\) in a simple way and offers for \(K^{-}\) a list of \(k\) which is complete up to one possible additional field (which he conjectures does not exist). In fact, \(K^{-}\) is related to the class number one problem. The set \(K^{+}\), related to the problem of the least quadratic nonresidue, is given conjecturally. [See also \textit{M. Leu}, Proc. Japan Acad., Ser. A 63, 323--326 (1987; Zbl 0659.12004) and Nagoya Math. J. 115, 185--198 (1989; Zbl 0659.12005).]
scientific article; zbMATH DE number 4081679