This is an appendix to the English translation of the book by A. A. Goldberg and I. V. Ostrovskii, Distribution of values of meromorphic functions, Moscow, Nauka, 1970. An English translation of this book is to be published soon by the AMS. In this appendix we survey the results obtained on the topics of the book after 1970. The literature on meromorphic functions is very large. There is a comp...

It is shown that the ideal theories of the fields of all meromorphic functions on any two noncompact Riemann surfaces are isomorphic. Further, various new representation and factorization theorems are proved. Introduction. Throughout this paper let X and Y denote noncompact (connected) Riemann surfaces. Let A(X) (or A for short), denote the ring of all analytic functions on X, and let F(X) (or ...

Using the results of third-order differential subordination, we introduce certain families admissible functions and discuss some applications subordination for meromorphic associated with a linear operator containing generalized Mittag-Leffler function.

We obtain a representation of the derivative of the spectral shift function ξ(λ, h) in the framework of semi-classical ”black box” perturbations. Our representation implies a meromorphic continuation of ξ(λ, h) involving the semi-classical resonances. Moreover, we obtain a Weyl type asymptotics of the spectral shift function as well as a Breit-Wigner approximation in an interval (λ− δ, λ+ δ), 0...

To shift the path of integration to the left, one needs at least meromorphic continuation to some half-plane R s > r− δ as well as some information on the growth and the distribution of the poles of Φr. Assuming the Riemann hypothesis, Egami and Matsumoto[4] described the behavior for the case r = 2. In addition to the RH, parts of their results depend on unproved assumptions on the distributio...