This article is concerned
with the number B𝒟(x) of integer points with relative prime coordinates in 𝒟,
where x is a large real variable and 𝒟 is a starlike set in the Euclidean plane.
Assuming the truth of the Riemann Hypothesis, we establish an asymptotic formula
for B𝒟(x). Applications to certain special geometric and arithmetic problems are
discussed.