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.To Professor Ekkehard Kratzel on his 70th birthday