Uniqueness theorems of meromorphic functions of a certain form

Junfeng Xu; Qi Han; Jilong Zhang

doi:10.4134/BKMS.2009.46.6.1079

Uniqueness theorems of meromorphic functions of a certain form

Junfeng Xu^*
, Qi Han
, Jilong Zhang

^*Corresponding author for this work

School of Mathematical Sciences

Wuyi University
University of Houston

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

3 Scopus citations

Abstract

In this paper, we shall show that for any entire function f, the function of the form f^m(fⁿ 1)f^′ has no non-zero finite Picard value for all positive integers m, n ∈ N possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if f^m(fⁿ-1)f^′ and g^m(gⁿ-1)g^′ share the value 1 weakly, then f ≡ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.

Original language	English
Pages (from-to)	1079-1089
Number of pages	11
Journal	Bulletin of the Korean Mathematical Society
Volume	46
Issue number	6
DOIs	https://doi.org/10.4134/BKMS.2009.46.6.1079
State	Published - 2009

Keywords

Entire function
Meromorphic function
Picard value

Access to Document

10.4134/BKMS.2009.46.6.1079

Cite this

@article{d5bcaeef1b5c4968b73b928da3e28be1,

title = "Uniqueness theorems of meromorphic functions of a certain form",

abstract = "In this paper, we shall show that for any entire function f, the function of the form fm(fn 1)f′ has no non-zero finite Picard value for all positive integers m, n ∈ N possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if fm(fn-1)f′ and gm(gn-1)g′ share the value 1 weakly, then f ≡ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.",

keywords = "Entire function, Meromorphic function, Picard value",

author = "Junfeng Xu and Qi Han and Jilong Zhang",

year = "2009",

doi = "10.4134/BKMS.2009.46.6.1079",

language = "英语",

volume = "46",

pages = "1079--1089",

journal = "Bulletin of the Korean Mathematical Society",

issn = "1015-8634",

publisher = "Korean Mathematical Society",

number = "6",

}

TY - JOUR

T1 - Uniqueness theorems of meromorphic functions of a certain form

AU - Xu, Junfeng

AU - Han, Qi

AU - Zhang, Jilong

PY - 2009

Y1 - 2009

N2 - In this paper, we shall show that for any entire function f, the function of the form fm(fn 1)f′ has no non-zero finite Picard value for all positive integers m, n ∈ N possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if fm(fn-1)f′ and gm(gn-1)g′ share the value 1 weakly, then f ≡ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.

AB - In this paper, we shall show that for any entire function f, the function of the form fm(fn 1)f′ has no non-zero finite Picard value for all positive integers m, n ∈ N possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if fm(fn-1)f′ and gm(gn-1)g′ share the value 1 weakly, then f ≡ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.

KW - Entire function

KW - Meromorphic function

KW - Picard value

UR - https://www.scopus.com/pages/publications/77749274573

U2 - 10.4134/BKMS.2009.46.6.1079

DO - 10.4134/BKMS.2009.46.6.1079

M3 - 文章

AN - SCOPUS:77749274573

SN - 1015-8634

VL - 46

SP - 1079

EP - 1089

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 6

ER -

Uniqueness theorems of meromorphic functions of a certain form

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this