Primitive lattice points inside an ellipse

Let Q(u, v) be a positive definite binary quadratic form with arbitrary real coefficients. For large real x , one may ask for the number B(x) of primitive lattice points (integer points ( m, n ) with gcd( M, n ) = 1) in the ellipse disc Q(u, v) ≤ x , in particular, for the remainder term R(x) in the asymptotics for B(x) . While upper bounds for R(x) depend on zero-free regions of the zeta-function, and thus, in most published results, on the Riemann Hypothesis, the present paper deals with a lower estimate. It is proved that the absolute value or R(x) is, in integral mean, at least a positive constant c time x 1/4 . Furthermore, it is shown how to find an explicit value for c , for each specific given form Q .