Advanced Search

Let F(X,Y) be an irreducible binary cubic form with integer coefficients and positive discriminant D. Let k be a positive integer satisfying $k<\left({\left(3D\right)}^{1/4}\right)/2\pi$. We give improved upper bounds for the number of primitive solutions of the Thue inequality $\left|F\right(X,Y\left)\right|\le k$.