Zhang, Keyu; Xu, HongYan; Yi, Hongxun Borel directions and uniqueness of meromorphic functions. (English) Zbl 1470.30030 Abstr. Appl. Anal. 2013, Article ID 793810, 8 p. (2013). Summary: We investigate the relationship between Borel directions and uniqueness of meromorphic functions and obtain some results of meromorphic functions sharing four distinct values IM and one set in an angular domain containing a Borel line. Our result is an improvement of a recent theorem given by J. Long and P. Wu [Chin. Ann. Math., Ser. A 33, No. 3, 261–266 (2012; Zbl 1274.30123)]. Cited in 1 Document MSC: 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D30 Meromorphic functions of one complex variable (general theory) Citations:Zbl 1274.30123 × Cite Format Result Cite Review PDF Full Text: DOI OA License References: [1] Hayman, W. K., Meromorphic Functions (1964), London, UK: Oxford University Press, London, UK · Zbl 0115.06203 [2] Yang, L., Value Distribution Theory (1993), Berlin, Germany: Springer/Science Press, Berlin, Germany · Zbl 0790.30018 [3] Lin, W. C.; Mori, S.; Tohge, K., Uniqueness theorems in an angular domain, The Tohoku Mathematical Journal, 58, 4, 509-527 (2006) · Zbl 1134.30026 · doi:10.2748/tmj/1170347687 [4] Nevanlinna, R., Le Théorème de Picard-Borel et la Théorie des Fonctions Méromorphes (1974), New York, NY, USA: Chelsea Publishing, New York, NY, USA · JFM 54.0349.07 [5] Yi, H.-X.; Yang, C.-C., Uniqueness Theory of Meromorphic Functions, 557 (2003), Dordrecht, The Netherlands: Kluwer Academic, Dordrecht, The Netherlands · Zbl 1070.30011 [6] Zheng, J.-H., On uniqueness of meromorphic functions with shared values in some angular domains, Canadian Mathematical Bulletin. Bulletin Canadien de Mathématiques, 47, 1, 152-160 (2004) · Zbl 1045.30019 · doi:10.4153/CMB-2004-016-1 [7] Zheng, J.-H., On uniqueness of meromorphic functions with shared values in one angular domain, Complex Variables. Theory and Application, 48, 9, 777-785 (2003) · Zbl 1041.30009 · doi:10.1080/02781070310001599368 [8] Cao, T.-B.; Yi, H.-X., On the uniqueness of meromorphic functions that share four values in one angular domain, Journal of Mathematical Analysis and Applications, 358, 1, 81-97 (2009) · Zbl 1167.30012 · doi:10.1016/j.jmaa.2009.04.043 [9] Wu, Z.-J., On uniqueness of meromorphic functions in an angular domain, Kodai Mathematical Journal, 30, 3, 352-360 (2007) · Zbl 1145.30012 · doi:10.2996/kmj/1193924939 [10] Wu, Z.-J.; Sun, D.-C., A remark on uniqueness theorems in an angular domain, Japan Academy. Proceedings A, 84, 6, 73-77 (2008) · Zbl 1157.30024 · doi:10.3792/pjaa.84.73 [11] Xu, H.-Y.; Cao, T.-B., Uniqueness of two analytic functions sharing four values in an angular domain, Annales Polonici Mathematici, 99, 1, 55-65 (2010) · Zbl 1206.30043 · doi:10.4064/ap99-1-5 [12] Xu, H.-Y.; Cao, T.-B., Analytic functions in the unit disc sharing values in a sector, Annales Polonici Mathematici, 103, 3, 263-275 (2012) · Zbl 1276.30047 · doi:10.4064/ap103-3-4 [13] Cartwright, M. L., On the directions of borel of functions which are regular and of finite order in an angle, Proceedings of the London Mathematical Society, S2-38, 1, 503-541 · JFM 61.0339.03 · doi:10.1112/plms/s2-38.1.503 [14] Hayman, W. K.; Wu, S. J., Value distribution theory and the research of Yang Lo, Science in China B, 53, 3, 513-522 (2010) · Zbl 1195.30005 · doi:10.1007/s11425-010-0045-3 [15] Linden, C. N., On a conjecture of Valiron concerning sets of indirect Borel points, Journal of the London Mathematical Society, 41, 304-312 (1966) [16] Valiron, G., Entire functions and Borel’s directions, Proceedings of the National Academy of Sciences of the United States of America, 20, 3, 211-215 (1934) · Zbl 0009.02503 [17] Wu, S. J., Further results on Borel removable sets of entire functions, Annales Academiae Scientiarum Fennicae A, 19, 1, 67-81 (1994) · Zbl 0791.30023 [18] Wu, S. J., The distribution of the Borel directions of entire functions, Chinese Annals of Mathematics A, 14, 4, 400-406 (1993) · Zbl 0785.30015 [19] Yang, L., Borel directions of meromorphic functions in an angular domain, Scientia Sinica. Zhongguo Kexue, 149-164 (1979) [20] Yang, L.; Zhang, G. H., Distribution of Borel directions of entire functions, Acta Mathematica Sinica. Shuxue Xuebao, 19, 3, 157-168 (1976) · Zbl 0351.30026 [21] Yang, L.; Zhang, G. H., Progress in the value distribution theory of meromorphic functions, Kexue Tongbao. Chinese Science Bulletin, 22, 9, 375-380 (1977) · Zbl 0435.30027 [22] Yang, L.; Chang, K. H., Sur la distribution des directions de Borel des fonctions méromorphes, Scientia Sinica, 16, 465-482 (1973) · Zbl 0338.30021 [23] Zhang, G. H., Common Borel directions of meromorphic functions and their successive derivatives or integrals. III, Acta Mathematica Sinica. Shuxue Xuebao, 20, 4, 237-247 (1977) · Zbl 0371.30028 [24] Zhang, Q. D., \(T\) direction and Borel direction of meromorphic functions of finite and positive order, Acta Mathematica Sinica. Chinese Series, 50, 2, 413-419 (2007) · Zbl 1121.30308 [25] Chuang, C. T., Singular Direction of Meromorpic Functions (1982), Beijing, China: Science Press, Beijing, China [26] Long, J. R.; Wu, P. C., Borel directions and uniqueness of meromorphic functions, Chinese Annals of Mathematics A, 33, 3, 261-266 (2012) · Zbl 1274.30123 [27] Goldberg, A. A.; Ostrovskiĭ, I. V., The Distribution of Values of Meromorphic Function, 592 (1970), Nauka, Moscow [28] Goldberg, A. A., Nevanlinna’s lemma on the logarithmic derivative of a meromorphic function, Mathematical Notes, 17, 4, 310-312 (1975) · Zbl 0316.30021 [29] Chuang, C. T., On Borel directions of meromorphic functions of infinite order. II, Bulletin of the Hong Kong Mathematical Society, 2, 2, 305-323 (1999) · Zbl 0940.30015 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.