INHOMOGENEOUS MINIMA OF A CLASS OF TERNARY QUADRATIC-FORMS

Let GAMMA2,1(k) denote the kth successive inhomogeneous minima for positive values of real indefinite ternary quadratic forms of type (2, 1). Here it is proved that for the class of zero forms GAMMA2,1(2) = 8/3, GAMMA2,1(3) = 9/4, GAMMA2,1(4) = 2. All the critical forms have also been obtained. GAMMA2,1(1) = 4 is already known. For non-zero forms it is proved that GAMMA2,1(1) < 10/3.