POSITIVE VALUES OF NONHOMOGENEOUS INDEFINITE QUADRATIC-FORMS OF TYPE (2, 5)

The minimum GAMMA(r,n-r) of positive values of non-homogeneous indefinite quadratic forms of type (r, n - r) is defined as the infimum of all constants GAMMA > 0 such that for any indefinite quadratic form Q of type (r, n - r) and determinant D not-equal 0 and any real numbers c1, ..., c(n) there exist integers x1, ..., x(n) such that 0 < Q(x1 + c1, ..., x(n) + c(n)) < (GAMMA\D\)1/n. In this paper it is proved that GAMMA2.5 = 32, thereby confirming the conjecture of Bambah, Dumir, and Hans-Gill. Also, all the critical forms for which equality is needed are determined. (C) 1994 Academic Press, Inc.