Gerald Kuba, Universität für Bodenkultur, Wien
Let be a real algebra of order where the basal units satisfy the primary Hamilton relations and The most important examples of such algebras are of course the division algebra of Hamilton's quaternions in dimension and the division algebra of Cayley's octaves in dimension . Further let be any integral domain, for instance the Lipschitz ring or the Hurwitz ring of integral quaternions in the case , or the subring in the case .
For a large positive parameter , let denote the number of squares with and all components of lying in the interval . Then, generalizing former results concerning the distribution of squares of Gaussian integers by H. Müller and W.G. Nowak, we show that