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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.54 no.1 Bogotá Jan./June 2020 

Original articles

On n-th roots of meromorphic maps

Sobre raíces n-ésimas de funciones meromorfas

Juan C. García1  * 

Rubén A. Hidalgo2 

1 Universidad Central del Ecuador, Quito, Ecuador

2 Universidad de La Frontera, Temuco, Chile


Let S be a connected Riemann surface and let φ: S → Ĉ be branched covering map of finite type. If n ≥ 2, then we describe a simple geometrical necessary and sufficient condition for the existence of some n-th root, that is, a meromorphic map ψ: S → Ĉ such that φ = ψ n .

Keywords: Riemann surfaces; holomorphic branched coverings; maps


Sea S una superficie de Riemann conexa y φ : S → Ĉ un cubrimiento ramificado holomorfo de tipo finito. Para cada n ≥ 2 describimos una condición geométrica necesaria y suficiente para la existencia de alguna raíz n-ésima, esto es, una función meromorfa ψ: S → Ĉ de manera que φ = ψ n .

Palabras clave: Superficies de Riemann; cubrimientos ramificados holomorfos; mapas

Full text available only in PDF format.


We thank the anonymous referee for her/his comments and suggestions which contributed to improving this manuscript.


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Received: December 06, 2019; Accepted: April 01, 2020

*Correspondencia: Juan C. García, Facultad de Ciencias, Universidad Central del Ecuador, Quito, Ecuador. Correo electrónico: DOI:

2010 Mathematics Subject Classification. 30F10, 57M12.

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