RT Journal Article
T1 On the asymptotics of visible elements and homogeneousequations in surface groups
A1 Antolín Pichel, Yago
A1 Ciobanu, Laura
A1 Viles, Noelia
AB Let F be a group whose abelianization is Zk, k  2. An element of F is calledvisible 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.
PB EMS Press
SN 1661-7207
YR 2012
FD 2012
LK https://hdl.handle.net/20.500.14352/43565
UL https://hdl.handle.net/20.500.14352/43565
LA eng
DS Docta Complutense
RD 6 abr 2025