Topological classification of conformal actions on cyclic p-gonal Riemann surfaces

A compact Riemann surface X of genus g>1 which can be realized as a p-sheeted covering of the Riemann sphere for some prime p is called p-gonal. If there is an automorphism of order p on X which permutes the sheets, we call X cyclic p-gonal. Here we classify conformal actions on cyclic p-gonal Riemann surfaces of genus g>2(p−1) up to topological conjugacy and determine which of them can be maximal.