Four counterexamples to Bloch’s principle

Rubel, Lee A.

doi:10.1090/S0002-9939-1986-0854029-2

Four counterexamples to Bloch’s principle
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by Lee A. Rubel

Proc. Amer. Math. Soc. 98 (1986), 257-260

DOI: https://doi.org/10.1090/S0002-9939-1986-0854029-2

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Abstract:

In this note, four counterexamples are given to Bloch’s heuristic principle in complex function theory. The first involves univalent functions, the second certain autonomous differential equations, and the remaining two involve certain autonomous differential expressions omitting certain values.

References

Étude sur les familles normales et les familles quasi-normales de fonctions méromorphes

62

W. K. Hayman, Research problems in function theory, The Athlone Press [University of London], London, 1967. MR 0217268

Un critère de normalité des familles de fonctions méromorphies

98

J. K. Langley, On normal families and a result of Drasin, Proc. Roy. Soc. Edinburgh Sect. A 98 (1984), no. 3-4, 385–393. MR 768358, DOI 10.1017/S0308210500013548
David Minda, A heuristic principle for a nonessential isolated singularity, Proc. Amer. Math. Soc. 93 (1985), no. 3, 443–447. MR 773999, DOI 10.1090/S0002-9939-1985-0773999-3
Abraham Robinson, Metamathematical problems, J. Symbolic Logic 38 (1973), 500–516. MR 337471, DOI 10.2307/2273049
Le Yang, Normal families and differential polynomials, Sci. Sinica Ser. A 26 (1983), no. 7, 673–686. MR 721287
Lo Yang, Meromorphic functions and their derivatives, J. London Math. Soc. (2) 25 (1982), no. 2, 288–296. MR 653387, DOI 10.1112/jlms/s2-25.2.288
Lawrence Zalcman, A heuristic principle in complex function theory, Amer. Math. Monthly 82 (1975), no. 8, 813–817. MR 379852, DOI 10.2307/2319796
Lawrence Zalcman, Modern perspectives on classical function theory, Rocky Mountain J. Math. 12 (1982), no. 1, 75–92. MR 649740, DOI 10.1216/RMJ-1982-12-1-75