Unit equations and Fermat surfaces in positive characteristic

Koymans, Peter; Pagano, Carlo

doi:10.4064/aa180605-23-5

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Unit equations and Fermat surfaces in positive characteristic

MPS-Authors

/persons/resource/persons248540

Pagano, Carlo
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.4064/aa180605-23-5
(Publisher version)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

arXiv:1806.01614.pdf
(Preprint), 209KB

Supplementary Material (public)

There is no public supplementary material available

Citation

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.

Cite as: https://hdl.handle.net/21.11116/0000-0006-9CF5-6

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