The Method Of Thue-Siegel For Binary Quartic Forms

Abstract

We will use Thue-Siegel method, based on Padé approximation via hypergeometric functions, to give upper bounds for the number of integral solutions to the equation $|F(x,y)|=1$ as well as the inequalities $|F(x,y)|\le h$, for a certain family of irreducible quartic binary forms.

arXiv commentA version of this paper is to appear in Acta. Arith