THE REPRESENTATION OF BINARY QUADRATIC-FORMS BY POSITIVE-DEFINITE QUATERNARY QUADRATIC-FORMS

A quadratic Z-lattice L of rank n is defined to be k-regular for a positive integer k less-than-or-equal-to if L globally represents all quadratic Z-lattices of rank k which are represented everywhere locally by L. It is shown that there exist only finitely many isometry classes of primitive positive definite quadratic Z-lattices of rank 4 which are 2-regular.