Cubic Thue inequalities with positive discriminant

Research paper by Shabnam Akhtari

Indexed on: 22 Jul '13Published on: 22 Jul '13Published in: Mathematics - Number Theory


We will give an explicit upper bound for the number of solutions to cubic inequality |F(x, y)| \leq h, where F(x, y) is a cubic binary form with integer coefficients and positive discriminant D. Our upper bound is independent of h, provided that h is smaller than D^{1/4}.