Number of solutions of cubic Thue inequalities with positive discriminant
Volume 171 / 2015
Acta Arithmetica 171 (2015), 81-95
MSC: Primary 11D45, 11D75; Secondary 11E76, 11D25.
DOI: 10.4064/aa171-1-6
Abstract
Let $F(X,Y)$ be an irreducible binary cubic form with integer coefficients and positive discriminant $D$. Let $k$ be a positive integer satisfying \[ k<\frac {(3D)^{1/4}}{2\pi }. \] We give improved upper bounds for the number of primitive solutions of the Thue inequality \[ |F(X,Y)|\leq k. \]
