Bujalance, E.Etayo Gordejuela, J. JavierGamboa Mutuberria, José ManuelGromadzki, G.2023-06-202023-06-202011E. Bujalance, J.J. Etayo, J.M. Gamboa, G. Gromadzki, Automorphism Groups of Compact Bordered Klein Surfaces, A Combinatorial Approach, in: Lecture Notes in Math., vol. 1439, Springer Verlag, 1990. G. Castelnuovo, Ricerche de geometria sulle curve algebriche, Atti Acad. Sci. Torino 24 (1889) 346–373. (Memorie Scelte, Zanichelli Bologna, 1937, pp. 19–44). H.M. Farkas, I. Kra, Riemann Surfaces, in: Graduate Text in Mathematics, Springer-Verlag, 1980. G. Gromadzki, A. Weaver, A. Wootton, On gonality of Riemann surfaces. Geom. Dedicata (in press). C. Maclachlan, Smooth coverings of hyperelliptic surfaces, Quart. J. Math. Oxford 22 (2) (1971) 117–123. H.H. Martens, A remark on Abel’s Theorem and the mapping of linear series, Comment. Math. Helv. 52 (1977) 557–559. F. Severi, Vorlesungen über algebraische Geometrie, Teubner, Leipzig (1921).0022-404910.1016/j.jpaa.2010.07.004https://hdl.handle.net/20.500.14352/42173A compact Riemann surface X of genus g ≥ 2 which can be realized as a q-fold, normal covering of a compact Riemann surface of genus p is said to be (q, p)-gonal. In particular the notion of (2, p)-gonality coincides with p-hyperellipticity and (q, 0)-gonality coincides with ordinary q-gonality. Here we completely determine the relationship between the gonalities of X and Y for an N-fold normal covering X → Y between compact Riemann surfaces X and Y. As a consequence we obtain classical results due to Maclachlan (1971) [5] and Martens (1977) [6].engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022404910001581http://www.sciencedirect.comrestricted access517.547MathematicsAppliedFunciones (Matemáticas)1202 Análisis y Análisis Funcional