Science in China Series A: Mathematics

, 43:1060

The error term in Nevanlinna’s inequality


DOI: 10.1007/BF02898240

Cite this article as:
Chen, H. & Ye, Z. Sci. China Ser. A-Math. (2000) 43: 1060. doi:10.1007/BF02898240


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.


meromorphic functionNevanlinna’s inequalityerror term

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