Inhomogeneous minimum of indefinite quadratic forms in five variables of type (4,1) or (1,4): a conjecture of Watson

Abstract

In the present paper it is proved that if Q(x, y, z, t, u) is a real indefinite quadratic form of type (4, 1) or (1.4) and determinant D, then for any real numbers X_o, Y_o, z_o, t_o, u_o there exist integers x, y, z, t, u such that I Q(x + x_o, y + y_o, z + z_o, t + t_o, u + u_o) I≤(½ I D I )^⅕. All the critical forms are also obtained.