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  Unit equations and Fermat surfaces in positive characteristic

Koymans, P., & Pagano, C. (2020). Unit equations and Fermat surfaces in positive characteristic. Acta Arithmetica, 193(2), 133-156. doi:10.4064/aa180605-23-5.

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Koymans-Pagano_Unit equations and Fermat surfaces in positive characteristic_2020.pdf (Publisher version), 451KB
 
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 Creators:
Koymans, Peter, Author
Pagano, Carlo1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory
 Abstract: In this article 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 $x^N + y^N + z^N = 1$.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 24
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 Table of Contents: -
 Rev. Type: Peer
 Degree: -

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Title: Acta Arithmetica
  Abbreviation : Acta Arith.
Source Genre: Journal
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Publ. Info: Institute of Mathematics, Polish Academy of Sciences
Pages: - Volume / Issue: 193 (2) Sequence Number: - Start / End Page: 133 - 156 Identifier: -