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