On the asymptotic values of meromorphic functions in the $n$-fold punctured plane - Arias, Arturo Fernández (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.5We present some results on the asymptotic paths and asymptotic values for meromorphic functions in the $n$-fold extended punctured plane $\widehat{\mathbb{C}}\backslash\{p_{1},…,p_{n}\} .$ These results extend some classical results obtained for analytic and meromorphic functions in the complex plane $\mathbb{C}.$ In particular, in this more general setting, we give a version of F. Iversen's result on the existence of asymptotic values for entire functions in the plane. We also obtain a bound for the number of isolated directly critical singularities of a meromorphic function of finite order $k$ and a finite number of poles.