Given a closed Riemann surface S together a group of its conformal automorphisms H ≅ Z22, it is known that there are Schottky uniformizations of S realizing H. In this note we proceed to give an explicit Schottky uniformizations for each of all different topological actions of Z22 as group of conformal automorphisms on a closed Riemann surface.
A complex polynomial is called a Hurwitz polynomial if all its roots have a real part smaller than zero. This kind of polynomial plays an all-dominant role in stability checks of electrical networks.In this article we prove Schur's criterion [17] that allows to decide whether a polynomial p(x) is Hurwitz without explicitly computing its roots: Schur's recursive algorithm successively constructs polynomials pi(x) of lesser degree by division with x - c, ℜ {c} < 0, such that pi(x) is Hurwitz if...
The paper discusses development of the theory of value distribution and growth of meromorphic functions, focusing on two basic notions: exceptional values and asymptotic values. Some historical context is given and contemporary achievements are presented. In particular, recent results concerning exceptional functions and asymptotic functions are considered.