Entire functions that share a set with their derivatives

Jianming Chang, Mingliang Fang, Lawrence Zalcman

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let f be a nonconstant entire function and let S = {a, b, c}, where a, b and c are distinct complex numbers. If E(S, f) = E(S, f'), then either (i) f = Ce z ; or (ii) f(z) = Ce z (a+b+c), (2a-b-c)(2b-c-a)(2c-a-b) = 0; or (iii) f(z) = Ce (a+b+c), 2 +c 2 -ab-bc-ca = 0, where C is a nonzero constant.

Original languageEnglish
Pages (from-to)561-569
Number of pages9
JournalArchiv der Mathematik
Volume89
Issue number6
DOIs
StatePublished - Dec 2007

Bibliographical note

Funding Information:
1Research suported by the NNSF of China (Grant No. 10471065). 2Research suported by the NNSF of China (Grant No. 10671093). 3Research supported by the German-Israeli Foundation for Scientific Research and Development, Grant G-809-234.6/2003. 4Research supported by the Fred and Barbara Kort Sino-Israel Post Doctoral Fellowship Program at Bar-Ilan University.

Keywords

  • Entire functions
  • Uniqueness theorem

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