ENTIRE FUNCTIONS SHARING ZERO CM WITH THEIR HIGH ORDER DIFFERENCE OPERATORS

In this paper, we investigate uniqueness of entire functions of order less than 2 sharing the value 0 with their difference operators and obtain a result as follows: Letfbe a transcendental entire function such thatσ(f) < 2 andλ(f) <σ(f). Iffand Δ n fshare the value 0 CM, thenfmust be form off...

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Published inTaiwanese journal of mathematics Vol. 18; no. 3; pp. 701 - 709
Main Authors Zhang, Jie, Zhang, Jianjun, Liao, Liangwen
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2014
Subjects
Entire functions
Mathematical constants
Mathematical functions
Mathematical induction
Mathematics
Meromorphic functions
Polynomials
Transcendentals
Uniqueness
Zero
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ISSN1027-5487
2224-6851
DOI10.11650/tjm.18.2014.3802

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Summary:In this paper, we investigate uniqueness of entire functions of order less than 2 sharing the value 0 with their difference operators and obtain a result as follows: Letfbe a transcendental entire function such thatσ(f) < 2 andλ(f) <σ(f). Iffand Δ n fshare the value 0 CM, thenfmust be form off(z) =Aeαz , whereAandαare two nonzero constants. This result confirms a conjecture posed earlier on the topic. 2010Mathematics Subject Classification: 30D35, 34M10. Key words and phrases: Uniqueness, Entire function, Difference equation, Order.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.18.2014.3802