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Unit equations and Fermat surfaces in positive characteristic

Volume 193 / 2020

Peter Koymans, Carlo Pagano Acta Arithmetica 193 (2020), 133-156 MSC: Primary 11D41; Secondary 11D61. DOI: 10.4064/aa180605-23-5 Published online: 17 January 2020


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 $x^N + y^N + z^N = 1$.


  • Peter KoymansMathematisch Instituut
    Leiden University
    Niels Bohrweg 1
    2333 CA Leiden, the Netherlands
  • Carlo PaganoMax Planck Institute for Mathematics
    Vivatsgasse 7
    53111 Bonn, Germany

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