Maximal order of automorphisms of trigonal Riemann surfaces

In this paper we find the maximal order of an automorphism of a trigonal Riemann surface of genus g, g⩾5. We find that this order is smaller for generic than for cyclic trigonal Riemann surfaces, showing that generic trigonal surfaces have “less symmetry” than cyclic trigonal surfaces. Finally we prove that the maximal order is attained for infinitely many genera in both the cyclic and the generic case.