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2012•Proceedings of the London Mathematical SocietyRequires access

Zeros of higher derivatives of meromorphic functions in the complex plane

Katsutoshi Yamanoi

Open publisher page 38 citations

Abstract

We prove the Gol’dberg conjecture, which states that the frequency of distinct poles of a meromorphic function f in the complex plane is governed by the frequency of zeros of the second derivative f″. As a consequence, we prove Mues’ conjecture concerning the defect relation for the derivatives of meromorphic functions in the complex plane.

About this research paper

What this paper is about

We prove the Gol’dberg conjecture, which states that the frequency of distinct poles of a meromorphic function f in the complex plane is governed by the frequency of zeros of the second derivative f″. As a consequence, we prove Mues’ conjecture concerning the defect relation for the derivatives of meromorphic functions in the complex plane.

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OpenAlex reports 38 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We prove the Gol’dberg conjecture, which states that the frequency of distinct poles of a meromorphic function f in the complex plane is governed by the frequency of zeros of the second derivative f″. As a consequence, we prove Mues’ conjecture concerning the defect relation for the derivatives of meromorphic functions in the complex plane.

Key concepts: Meromorphic function, Complex plane, Conjecture, Mathematics, Plane (geometry), Pure mathematics, Derivative (finance), Function (biology)

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