Yang, Pai; Niu, Peiyan Derivatives of meromorphic functions with multiple zeros and small functions. (English) Zbl 1470.30027 Abstr. Appl. Anal. 2014, Article ID 310251, 10 p. (2014). Summary: Let \(f \left(z\right)\) be a meromorphic function in \(\mathbb C\), and let \(\alpha \left(z\right) = R \left(z\right) h \left(z\right) \not\equiv 0\), where \(h \left(z\right)\) is a nonconstant elliptic function and \(R \left(z\right)\) is a rational function. Suppose that all zeros of \(f \left(z\right)\) are multiple except finitely many and \(T \left(r, \alpha\right) = o \left\{T \left(r, f\right)\right\}\) as \(r \rightarrow \infty\). Then \(f' \left(z\right) = \alpha \left(z\right)\) has infinitely many solutions. Cited in 2 Documents MSC: 30D30 Meromorphic functions of one complex variable (general theory) 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D45 Normal functions of one complex variable, normal families × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Hayman, W. K., Picard values of meromorphic functions and their derivatives, Annals of Mathematics, 70, 1, 9-42 (1959) · Zbl 0088.28505 [2] Wang, Y. F.; Fang, M. L., Picard values and normal families of meromorphic functions with multiple zeros, Acta Mathematica Sinica, 14, 1, 17-26 (1998) · Zbl 0909.30025 [3] Pang, X. C.; Nevo, S.; Zalcman, L., Derivatives of meromorphic functions with multiple zeros and rational functions, Computational Methods and Function Theory, 8, 2, 483-491 (2008) · Zbl 1149.30023 [4] Akhiezer, N. I., Elements of the Theory of Elliptic Functions, 1970. Moscow. Elements of the Theory of Elliptic Functions, 1970. Moscow, Translated Into English as AMS Translations of Mathematical Monographs, 79 (1990), Rhode Island, RI, USA: AMS, Rhode Island, RI, USA · Zbl 0694.33001 [5] Pang, X. C.; Zalcman, L., Normal families and shared values, Bulletin of the London Mathematical Society, 32, 3, 325-331 (2000) · Zbl 1030.30031 [6] Yang, P.; Nevo, S., Derivatives of meromorphic functions with multiple zeros and elliptic functions, Acta Mathematica Sinica, 29, 7, 1257-1278 (2013) · Zbl 1288.30028 [7] Xu, Y., Normal families and exceptional functions, Journal of Mathematical Analysis and Applications, 329, 2, 1343-1354 (2007) · Zbl 1154.30306 · doi:10.1016/j.jmaa.2006.07.021 [8] Bank, S. B.; Langley, J. K., On the value distribution theory of elliptic functions, Monatshefte für Mathematik, 98, 1, 1-20 (1984) · Zbl 0545.30023 · doi:10.1007/BF01536904 [9] Pang, X. C.; Nevo, S.; Zalcman, L., Quasinormal families of meromorphic functions II, Operator Theory, 158, 177-189 (2005) · Zbl 1088.30026 [10] Pang, X. C.; Yang, D. G.; Zalcman, L., Normal families and omitted functions, Indiana University Mathematics Journal, 54, 1, 223-235 (2005) · Zbl 1077.30026 · doi:10.1512/iumj.2005.54.2492 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.