Acta mathematica scientia, Series B >
ON UNIQUENESS FOR ALGEBROID FUNCTIONS OF FINITE ORDER
Received date: 2014-03-05
Online published: 2015-05-01
Supported by
The work of second author was partially supported by Natural Science Foundation of China (11271227) and PCSIRT (IRT1264).
Guided by Lo.Yang's method, we concern the question that how algebroid functions are determined by their multiple values and deficient values and we prove an at most 3v-valued theorem for algebroid functions. The results are complemented by an example for completeness.
Key words： Algebroid functions; value distribution; multiple values; deficient values
Pingyuan ZHANG , Peichu HU . ON UNIQUENESS FOR ALGEBROID FUNCTIONS OF FINITE ORDER[J]. Acta mathematica scientia, Series B, 2015 , 35(3) : 630 -638 . DOI: 10.1016/S0252-9602(15)30009-6
[1] Ullrich E. Uber den Einfluess der verzweigtheit einer algebloide auf ihre wertverteilung. J Reine Angew Math, 1931, 169: 198-220
[2] Valiron G. Sur quelques propriétés des fonctions algébro¨ldes. Comptes Rendus Math, 1929, 189: 824-826
[3] Xuan Zuxing, Gao Zongsheng. Uniqueness theorems for algebroid functions. Complex Var and Ell Eq, 2006, 51(7): 701-712
[4] Gol'dberg A A, P'yana V A. Uniqueness theorems for rational, algebraic, and algebroid functions. Ukrainian Math J, 1994, 46: 219-235
[5] He Yuzan. A uniqueness theorem of algebroid functions and systems of holomorphic functions. Pure Appl Math, 1985, (1): 24-31
[6] Sun Daochun, Gao Zongsheng. On the operations of algebroid functions. Acta Math Sci, 2010, 30B(1): 247-256
[7] Eremenko A E. Meromorphic solutions of algebraic differential equations. Uspekhi Mat Nauk, 1982, 37(4): 53-82
[8] He Yuzan, Xiao Xiuzhi. Algebroid function and ordinary differential equations (in chinese). Beijing: Science Press, 1988
[9] Yi Hongxun, Yang C C. Uniqueness theory of meromorphic functions. Beijing: Science Press, 1995
[10] Prokoporich G S. Fix-points of meromorphic functions. Ukrainina Math J, 1973, 25(2): 248-260
[11] Ueda H. Unicity theorems for meromorphic or entire functions. Kodai Math J, 1980, 3(3): 457-471
[12] Zhang Qingcai. Borels directions and shared values. Acta Mathematica Scientia, 2013, 33B(2): 471-483
[13] Deng Hongcun. A note on complete manifolds with finite volume. Acta Mathematica Scientia, 2014, 34B(3): 807-813
[14] Liu Huifang, Sun Daochun. On the sharing values of Algebriod functions and their derivatives. Acta Mathematica Scientia, 2013, 33B(1): 268-278
/
| 〈 |
|
〉 |