Entire functions that share real zeros and real ones

Conformal Mappings And Entire Functions With Real Zeros

Differential operators and entire functions with simple real zeros

Let φ and f be functions in the Laguerre–Pólya class. Write φ(z) = e−αzφ1(z) and f (z) = e−βzf1(z), where φ1 and f1 have genus 0 or 1 and α,β 0. If αβ < 1/4 and φ has infinitely many zeros, then φ(D)f (z) has only simple real zeros, where D denotes differentiation.  2004 Elsevier Inc. All rights reserved.

Real entire functions with real zeros and a conjecture of Wiman

This conclusion is not true for the first derivative as the example exp(sin z) shows. For real entire functions with finitely many zeros, all of them real, Theorem 1.1 was proved in [3]. Theorem 1.1 can be considered as an extension to functions of infinite order of the following result of Sheil-Small [20], conjectured by Wiman in 1914 [1, 2]. For every integer p ≥ 0, denote by V2p the set of e...

Entire Functions That Share Rational Functions with Their Derivatives

In this paper, we use the idea of normal family to deal with the uniqueness problems of entire functions that share a rational function with its derivative and get a uniqueness theorem. The conclusions in this paper can be used to improve several known results. Some examples are provided to show that the results presented in this paper are possible. AMS Mathematics Subject Classification (2010)...

Non-real Zeros of Derivatives of Real Meromorphic Functions

The main result of the paper determines all real meromorphic functions f of finite order in the plane such that f ′ has finitely many zeros while f and f(k), for some k ≥ 2, have finitely many non-real zeros. MSC 2000: 30D20, 30D35.