Representations of binary forms by certain quinary positive integral quadratic forms

Abstract

In this article, we provide the complete answer to a question raised by Kitaoka in his book. (1999, "Arithmetic of Quadratic Forms," Cambridge Univ. Press, Cambridge, UK). More precisely, we prove that A(4) perpendicular to [4] represents all but one and D(4)20[21/2] represents all but three binary positive even Z-lattices. We further investigate representations of the binary forms by quinary forms in certain positive even 2-universal genera of class number 2. (C) 2001 Academic Press.