Cyclic covering of the projective line with prime gonality

Let V be a cyclic covering of the complex projective line, g be the genus of V  , Gon(V)Gon(V) be the gonality of V, and p   be a prime number. In this note, we prove a necessary and sufficient condition for Gon(V)=pGon(V)=p when g>(p−1)2g>(p−1)2. We also give a necessary and sufficient condition without the bound of g   for the case where p=3p=3, and the similar result for the case where p=2p=2 has been given in the previous notes [3] and [4].