Non-real zeros of derivatives in the unit disc

James Langley

Non-real zeros of derivatives in the unit disc

Complex Variables 2024-03-29 v1

Authors: James Langley

Abstract

The main result establishes an estimate for the growth of a real meromorphic function $f$ on the unit disc $\Delta$ such that: (i) at least one of $f$ and $1/f$ has finitely many poles and non-real zeros in $\Delta$ ; (ii)~ $f^{(k)}$ has finitely many non-real zeros in $\Delta$ , for some $k \geq 2$ .

Keywords

meromorphic function zeros of derivatives unit disc complex analysis

Cite

@article{arxiv.2403.19403,
  title  = {Non-real zeros of derivatives in the unit disc},
  author = {James Langley},
  journal= {arXiv preprint arXiv:2403.19403},
  year   = {2024}
}

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