Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  078.26301
Autor:  Erdös, Pál; Rényi, Alfréd
Title:  On the number of zeros of successive derivatives of entire functions of finite order. (In English)
Source:  Acta Math. Acad. Sci. Hung. 8, 223-225 (1957).
Review:  Set f(z) be an entire function, M(r) = max|z| = r |f(z)|, x = H(y) the inverse function of y = log M(x), Nk(f(z),1) the number of zeros of f(k) (z) in the unit circle. Then

limsupk ––> oo k-1 Nk(f(z),1) H(k) \leq e2-\rho^{-1}

when f(z) is of finite order \rho \geq 1. Compare the author's paper (see Zbl 070.29601), where e2 appears on the R. H. S. of the inequality and \rho is unrestricted.
Reviewer:  N.A.Bowen
Classif.:  * 30D20 General theory of entire functions
                   30C15 Zeros of polynomials, etc. (one complex variable)
Index Words:  Theory of Functions

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