POSITIVE VALUES OF NONHOMOGENEOUS INDEFINITE QUADRATIC-FORMS OF TYPE-(1,4)

Let GAMMA(r,n-r) denote the infimum of all numbers GAMMA > 0 such that for any real indefinite quadratic Q in n variables of type (r,n - r), determinant D not-equal 0 and real numbers c1,...,c(n) there exist (x1,..,x(n)) = (c1,...,c(n) (mod 1) satisfying 0 < Q(x1,...,x(n)) less-than-or-equal-to (GAMMA\D\)1/n. All the values of GAMMA(r,s) are known except GAMMA1,4. It is shown that 8 less-than-or-equal-to GAMMA1,4 less-than-or-equal-to 16.