On the distribution of zeros of analytic functions in angles in \(\mathbf{C} \backslash \{ {0}\} \)

Abstract

In this article some results on the value distribution theory of analytic functions defined in angles of \(\mathbb{C}\), due mainly to B. Ja. Levin and A. Pfluger, will be extended to the more general situation where the functions are defined in angles of \(\mathbb{C}\backslash\{ 0\}\). More precisely, angles \(S ( \theta_{1},\theta_{2}) \) with vertex at the origin will be considered and where a singularity at zero is allowed. An special class of these functions are those of completely regular growth for which it is proved a basic result which yields an expression of the density of its zeros in terms of the indicator function.