The error term in Nevanlinna’s inequality

Article

Abstract

An upper bound is given for the error termS(r, |aj|,f) in Nevanlinna’s inequality. For given positive increasing functions p and $ with ∫1 dr/p(r) = ∫1 dr/rϕ(r) = ∞, setP(r) = ∫1r dt/p,Ψ(r) = ∫1r dt/tϕ(t) We prove that
$$S(r, \left\{ {a_j } \right\}, f) \leqslant \log \frac{{T(r, f)\phi (T(r, f))}}{{p(r)}} + O(1)$$
holds, with a small exceptional set of r, for any finite set of points |aj| in the extended plane and any meromorphic function f such thatΨ(T(r, f)) =O(P(r)). This improves the known results of A. Hinkkanen and Y. F. Wang. The sharpness of the estimate is also considered.

Keywords

meromorphic function Nevanlinna’s inequality error term 

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Copyright information

© Science in China Press 2000

Authors and Affiliations

  1. 1.Department of MathematicsNanjing Normal UniversityNanjingChina
  2. 2.Department of Mathematical SciencesNorthern Illinois UniversityDe KalbUSA

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