A family of $(p,n)$-gonal Riemann surfaces with several $(p,n)$-gonal groups

Abstract

Let $p \geqslant 3$ be a prime number and let $n \geqslant 0$ be an integer such that $p-1$ divides $n.$ In this short note we construct a family of $(p,n)$-gonal Riemann surfaces of maximal genus $2np+(p-1)^2$ with more than one $(p,n)$-gonal group.