Unit equations and Fermat surfaces in positive characteristic
Volume 193 / 2020
Acta Arithmetica 193 (2020), 133-156
MSC: Primary 11D41; Secondary 11D61.
DOI: 10.4064/aa180605-23-5
Published online: 17 January 2020
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 of solutions. We also apply these techniques to study the Fermat surface $x^N + y^N + z^N = 1$.
