Note on the Nevannlinna proximity function
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- by John L. Lewis PDF
- Proc. Amer. Math. Soc. 69 (1978), 129-134 Request permission
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
- Meledath Damodaran, On the distribution of values of meromorphic functions of slow growth, Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976) Lecture Notes in Math., Vol. 599, Springer, Berlin, 1977, pp. 17–21. MR 0450558
- David Drasin and Allen Weitsman, The growth of the Nevanlinna proximity function and the logarithmic potential, Indiana Univ. Math. J. 20 (1970/71), 699–715. MR 283200, DOI 10.1512/iumj.1971.20.20056
- W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 69 (1978), 129-134
- MSC: Primary 30A70; Secondary 30A68
- DOI: https://doi.org/10.1090/S0002-9939-1978-0499158-6
- MathSciNet review: 0499158