Unit equations and Fermat surfaces in positive characteristic

Acta Arithmetica, vol. 193, pp. 133–156

Abstract

We study the three-variable unit equation $x + y + z = 1$ to be solved in $x, y, z \in \mathcal {O}_S^\ast $, where $\mathcal {O}_S^\ast $ is the $S$-unit group of some global function field. We give upper bounds for the height of solutions and the number

Authors 2

1. Peter Koymans Aachen

   Leiden University

   Affiliation as printed

   Mathematisch Instituut Leiden University Niels Bohrweg 1 2333 CA Leiden, the Netherlands

2. Carlo Pagano

   Max Planck Institute for Mathematics

   Affiliation as printed

   Max Planck Institute for Mathematics Vivatsgasse 7 53111 Bonn, Germany

   #N# Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany