THE GENERALIZED THUE INEQUALITY

Let F((x) double under bar) = F(x, y) be a form in Z[x, y] of degree r greater than or equal to 3 and without multiple factors. A generaliza tion of the classical Thue inequality \F((x) double under bar\ less th an or equal to h is the inequality \F((x) double under bar)\ less than or equal to h\(x) double under bar\(gamma) where \(x) double under ba r is the maximum norm. When gamma < r-2 this inequality has only finit ely many solutions in integers. The present paper deals with upper bou nds for the number of such solutions.