Abstract
The Nevanlinna characteristic of a nonconstant elliptic function φ (z) satisfiesT(r, φ)=Kr 2 (1+o(1)) asr→∞ whereK is a nonzero constant. In this paper, we completely answer the following question: For which polynomialsQ(z, u 0,...,u n ) inu 0,...,u n , having coefficientsa(z) satisfyingT(r, a)=o(r 2) asr→∞, will the meromorphic functionh Q (z)=Q(z, ϕ(z),...,ϕ(n)(z)) either be identically zero or satisfyN(r, 1/h Q )=o(r 2) asr→∞? In fact, we answer this question for rational functionsQ(z, u 0,...,u n ) inu 0,...,u n , and also obtain analogous results for the Weierstrass functions ζ(z) and σ(z).
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This research was supported in part by the National Science Foundation (MCS82-00497).
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Bank, S.B., Langley, J.K. On the value distribution theory of elliptic functions. Monatshefte für Mathematik 98, 1–20 (1984). https://doi.org/10.1007/BF01536904
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DOI: https://doi.org/10.1007/BF01536904