Estimates of higher derivatives of meromorphic functions and the multiple points in the second main theorem of R. Nevanlinna. (English) Zbl 0949.30027

Barsegian, G. A.

Bull. Hong Kong Math. Soc. 2, No. 2, 341-345 (1999).

In this article, the author continues his recent investigations based on J. Lond. Math. Soc., II. Ser. 34, 534-540 (1986; Zbl 0608.30034)]. The idea here is to offer an upper bound for \(w^{(n)}(z)\), \(n>1\), on sets of \(a\)-points of a meromorphic function \(w(z)\). The upper bound is given in terms of \(|w'(z)|\) on the same set. Further results in this paper generalize the classical Nevanlinna result on totally ramified values of \(w(z)\). Due to relatively complicated notations, we refer to the original paper on details.

Reviewer: I.Laine (Joensuu)

MSC:

30D35

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

Citations:

Zbl 0608.30034