Yi, Hong-Xun; Lin, Wei-Chuan Uniqueness theorems concerning a question of Gross. (English) Zbl 1112.30028 Proc. Japan Acad., Ser. A 80, No. 7, 136-140 (2004). Summary: In this paper, we deal with the problem of uniqueness of meromorphic functions concerning one question of Gross, and obtain some results that are improvements of that of former authors. Moreover, the example shows that the result is sharp. Cited in 1 ReviewCited in 11 Documents MSC: 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory PDF BibTeX XML Cite \textit{H.-X. Yi} and \textit{W.-C. Lin}, Proc. Japan Acad., Ser. A 80, No. 7, 136--140 (2004; Zbl 1112.30028) Full Text: DOI Euclid References: [1] Frank, G., and Reinders, M.: A unique range set for meromorphic functions with 11 elements. Complex Variables Theory Appl., 37 , 185-193 (1998). · Zbl 1054.30519 [2] Fujimoto, H.: On uniqueness of meromorphic functions sharing finite sets. Amer. J. Math., 122 , 1175-1203 (2000). · Zbl 0983.30013 [3] Gross, F.: Factorization of meromorphic functions and some problems. In Complex Analysis (Proc. Conf. Univ. Kentucky, Lexington, KY, 1976), Lecture Notes Math., vol. 599, Springer-Verlag, Berlin-Heidelberg-New York, pp. 51-69 (1977). · Zbl 0357.30007 [4] Hayman, W. K.: Meromorphic Functions. Clarendon Press, Oxford (1964). · Zbl 0115.06203 [5] Laine, I.: Nevanlinna Theory and Complex Differential Equations. Studies in Mathematics, 15, Walter de Gruyter, New York (1993). · Zbl 0784.30002 [6] Li, P., and Yang, C. C.: On the unique range set of meromorphic functions. Proc. Amer. Math. Soc., 124 , 177-185 (1996). · Zbl 0845.30018 [7] Liao, L., and Yang, C. C.: On the cardinality of the unique range set for meromorphic and entire functions. Indian J. Pure Appl. Math., 31 , 431-440 (2000). · Zbl 0979.30019 [8] Mues, E., and Reinders, M.: Meromorphic functions sharing one value and unique range sets. Kodai Math. J., 18 , 515-522 (1995). · Zbl 0919.30023 [9] Yang, C. C., and Hua, X. H.: Uniqueness and value-sharing of meromorphic functions. Ann. Acad. Sci. Fenn. Math., 22 , 395-406 (1997). · Zbl 0890.30019 [10] Yang, L. Z.: Meromorphic functions that share two values. J. Math. Anal. Appl., 209 , 542-550 (1997). · Zbl 0941.30021 [11] Yi, H.-X.: Uniqueness of meromorphic functions and a question of Gross. Sci. China Ser. A 37 (7), 802-813 (1994). · Zbl 0821.30024 [12] Yi, H.-X.: Unicity theorems for meromorphic or entire functions. Bull. Austral. Math. Soc., 49 , 257-265 (1994). · Zbl 0809.30024 [13] Yi, H.-X.: Meromorphic functions that share one or two values. Complex Variables Theory Appl., 28 , 1-11 (1995). · Zbl 0841.30027 [14] Yi, H.-X.: Unicity theorems for meromorphic or entire functions. II. Bull. Austral. Math. Soc., 52 , 215-224 (1995). · Zbl 0844.30022 [15] Yi, H.-X.: Unicity theorems for meromorphic or entire functions. III. Bull. Austral. Math. Soc., 53 , 71-82 (1996). · Zbl 0855.30025 [16] Yi, H.-X.: On a question of Gross concerning uniqueness of entire functions. Bull. Austral. Math. Soc., 57 , 343-349 (1998). · Zbl 0905.30026 [17] Yi, H.-X., and Yang, C. C.: Uniqueness Theory of Meromorphic Functions. Pure and Applied Math. Monographs no.,32, Science Press, Beijing (1995). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.