Exceptional integers of some ternary quadratic forms
An integer \(c\), if everywhere locally representable by an integral ternary quadratic form, is known to be either representable by every form or by precisely half of all the inequivalent forms in the genus \(\mathrm{gen}(f)\) of \(f\). In the latter case such an integer will be called an exceptional integer for \(\mathrm{gen}(f)\). An integer \(c\) is called an exceptional integer for \(g\), \(g\in\mathrm{gen}(f)\), if \(g\) belongs to the``bad'' half-genus that fails to represent \(c\), i.e. if \(c\) is representable by some form in the genus but not by \(g\) itself. The paper gives characterizations for exceptional integers for ternary unimodular lattices. Especially the question: ``Which formally nonreal algebraic number field \(k\) has all its integers expressible as sums of three integral squares in \(k\)'' is in principle completely solved and explicitly solved for complex quadratic fields.
scientific article; zbMATH DE number 3775628