Abstract
Let be a family of meromorphic functions defined in D, all of whose zeros have multiplicity at least k+1. Let a and b be distinct finite complex numbers, and let k be a positive integer. If, for each pair of functions f and g in , f(k) and g(k) share the set S={a,b}, then is normal in D. The condition that the zeros of functions in have multiplicity at least k+1 cannot be weakened.
Original language | English |
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Pages (from-to) | 339-354 |
Number of pages | 16 |
Journal | Journal of the Australian Mathematical Society |
Volume | 86 |
Issue number | 3 |
DOIs | |
State | Published - Jun 2009 |
Bibliographical note
Funding Information:The research of the first author was supported by the NNSF of China (Grant No. 10771076) and the NSF of Guangdong Province, China. The research of the second author was supported by the German–Israeli Foundation for Scientific Research and Development, Grant G-809-234.6/2003. ©c 2009 Australian Mathematical Society 1446-7887/2009 $16.00
Funding
The research of the first author was supported by the NNSF of China (Grant No. 10771076) and the NSF of Guangdong Province, China. The research of the second author was supported by the German–Israeli Foundation for Scientific Research and Development, Grant G-809-234.6/2003. ©c 2009 Australian Mathematical Society 1446-7887/2009 $16.00
Funders | Funder number |
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German-Israeli Foundation for Scientific Research and Development | G-809-234.6/2003 |
NSF of Guangdong Province | |
National Natural Science Foundation of China | 10771076 |
Keywords
- Meromorphic function
- Normality
- Shared set.