2026-06-27T16:21:53Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/435652023-08-28T10:07:44Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Antolín Pichel, Yago author Ciobanu, Laura author Viles, Noelia author 2012 Let F be a group whose abelianization is Zk, k 2. An element of F is called visible if its image in the abelianization is visible, that is, the greatest common divisor of its coordinates is 1. In this paper we compute three types of densities, annular, even and odd spherical, of visible elements in surface groups. We then use our results to show that the probability of a homogeneous equation in a surface group to have solutions is neither 0 nor 1, as the lengths of the right- and left-hand side of the equation go to infinity. 1661-7207 10.4171/GGD/167 https://hdl.handle.net/20.500.14352/43565 https://doi.org/10.4171/GGD/167 On the asymptotics of visible elements and homogeneous equations in surface groups