Entire functions that share a set with their derivatives

Jianming Chang; Mingliang Fang; Lawrence Zalcman

doi:10.1007/s00013-007-2423-9

Entire functions that share a set with their derivatives

Jianming Chang
, Mingliang Fang
, Lawrence Zalcman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 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 language	English
Pages (from-to)	561-569
Number of pages	9
Journal	Archiv der Mathematik
Volume	89
Issue number	6
DOIs	https://doi.org/10.1007/s00013-007-2423-9
State	Published - 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.

Funding

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.

Funders	Funder number
Fred and Barbara Kort Sino–Israel Post Doctoral Fellowship Program at Bar-Ilan University
German-Israeli Foundation for Scientific Research and Development	G-809-234.6/2003
National Natural Science Foundation of China	10671093, 10471065

Keywords

Entire functions
Uniqueness theorem

Access to Document

10.1007/s00013-007-2423-9

Cite this

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title = "Entire functions that share a set with their derivatives",

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.",

keywords = "Entire functions, Uniqueness theorem",

author = "Jianming Chang and Mingliang Fang and Lawrence Zalcman",

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.",

year = "2007",

month = dec,

doi = "10.1007/s00013-007-2423-9",

language = "אנגלית",

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AU - Fang, Mingliang

AU - Zalcman, Lawrence

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PY - 2007/12

Y1 - 2007/12

N2 - 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.

AB - 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.

KW - Entire functions

KW - Uniqueness theorem

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SN - 0003-889X

VL - 89

SP - 561

EP - 569

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 6

ER -

Entire functions that share a set with their derivatives

Abstract

Bibliographical note

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Keywords

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