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The present work completes the classification of the compact Riemann surfacesof genus g with an analytic automorphism of order p (prime number) and p > g.More precisely, we construct a parameteriza- tion space for them, we computetheir groups of uniformization and we compute their full automorphism groups.Also, we give affine equations for special cases and some implications on thecomponents of the singular locus of the moduli space of smooth curves of genusg.Comment: 28 pages, 5 figure

Riemann surfaces of genus g with an automorphism of order p prime and p > g