On the number of solutions of Thue equations.

Let F(x,y) be an irreducible binary form of degree r≥3, with rational integral coefficients. Let N_r be the number of solutions of the equation |F(x,y)| = 1, then using the methods developed by Bombieri, Schmidt and Stewart, we prove that N_r<414r for r≥24 and that N_r<375r for r≥100. For 4≤r≤23, we obtain an upper bound of N_r for F with large discriminant. [ABSTRACT FROM AUTHOR]