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 in | Taiwanese journal of mathematics Vol. 18; no. 3; pp. 701 - 709 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Mathematical Society of the Republic of China
01.06.2014
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 1027-5487 2224-6851 |
| DOI | 10.11650/tjm.18.2014.3802 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Zhang, Jianjun Liao, Liangwen Zhang, Jie |
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| Cites_doi | 10.1017/S0305004106009777 10.1007/BF02565929 10.3792/pjaa.83.148 10.1007/BF03322176 10.1007/s11425-014-4848-5 10.1007/s00013-009-2895-x 10.1007/s11139-007-9101-1 |
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| SubjectTerms | Entire functions Mathematical constants Mathematical functions Mathematical induction Mathematics Meromorphic functions Polynomials Transcendentals Uniqueness Zero |
| Title | ENTIRE FUNCTIONS SHARING ZERO CM WITH THEIR HIGH ORDER DIFFERENCE OPERATORS |
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