Journal d’Analyse Mathématique

, Volume 71, Issue 1, pp 87–102

Sharp forms of nevanlinna’s error terms

Article

Abstract

Let f(z) be a meromorphic function in the plane. If ψ(t)/t andp(t) are two positive, continuous and non-decreasing functions on [1,∞) with ∫1dt/ψ(t) = ∞ and ∫1dt/p(t) = ∞, then\(S(r,f) \le \log + \frac{{\psi \left( {T(r,f)} \right)}}{{p(r)}} + O(1)\) asr → ∞ outside a small exceptional set, provided that the divergence of the integral ∫1rdt/ψ(t) is slow enough. The same forms for the logarithmic derivative and for the ramification term are obtained. It is shown by example that the estimates are best possible.

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Copyright information

© Hebrew University of Jerusalem 1997

Authors and Affiliations

  1. 1.Fachbereich 3 MathematikTechnische UniversitÄt BerlinBerlinGermany
  2. 2.Institute of MathematicsAcademia SinicaBeijingChina

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