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Proceedings of the American Mathematical Society

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Note on the Nevannlinna proximity function


Author: John L. Lewis
Journal: Proc. Amer. Math. Soc. 69 (1978), 129-134
MSC: Primary 30A70; Secondary 30A68
MathSciNet review: 0499158
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Abstract: Let $ \lambda $ be a positive function on $ (0,\infty )$ with $ {\lim _{r \to \infty }}\lambda (r) = \infty $, and A an arbitrary set of capacity zero. An example is given of a meromorphic function f for which $ m(r,a) \to \infty ,r \to \infty $, whenever $ a \in A$, and $ T(r,f) = O[{(\log r)^2}\lambda (r)],r \to \infty $ .


References [Enhancements On Off] (What's this?)

  • [1] Meledath Damodaran, On the distribution of values of meromorphic functions of slow growth, Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), Springer, Berlin, 1977, pp. 17–21. Lecture Notes in Math., Vol. 599. MR 0450558
  • [2] David Drasin and Allen Weitsman, The growth of the Nevanlinna proximity function and the logarithmic potential, Indiana Univ. Math. J. 20 (1970/1971), 699–715. MR 0283200
  • [3] W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0499158-6
Keywords: Meromorphic function, Nevanlinna proximity function, capacity
Article copyright: © Copyright 1978 American Mathematical Society