The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\)

Kontogeorgis, Aristides I.

Abstract

We study the group of automorphisms of the function fields of the curves \(x^n+y^m-1=0\) This group is bigger than \(\mu(m)\times \mu(n)\) in case \(m | n\). If moreover \(n-1\) is a power of the characteristic, then the group order exceeds the Hurwitz bound