Iteration and the zeros of the second derivative of a meromorphic function

A. Hinkkanen

doi:10.1112/plms/s3-65.3.629

Iteration and the zeros of the second derivative of a meromorphic function

A. Hinkkanen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Suppose that f =(f₁/f₂)e^p where the f_i are real entire functions of order less than n with only finitely many non-real zeros and P is a real polynomial of degree n. Suppose thatf₁ or f₂ is a polynomial. It is shown that f” has at least n - 2 distinct non-real zeros. The proof is based on the iteration of transcendental meromorphic functions.

Original language	English (US)
Pages (from-to)	629-650
Number of pages	22
Journal	Proceedings of the London Mathematical Society
Volume	s3-65
Issue number	3
DOIs	https://doi.org/10.1112/plms/s3-65.3.629
State	Published - Nov 1992

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General Mathematics

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abstract = "Suppose that f =(f1/f2)ep where the fi are real entire functions of order less than n with only finitely many non-real zeros and P is a real polynomial of degree n. Suppose thatf1 or f2 is a polynomial. It is shown that f” has at least n - 2 distinct non-real zeros. The proof is based on the iteration of transcendental meromorphic functions.",

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N2 - Suppose that f =(f1/f2)ep where the fi are real entire functions of order less than n with only finitely many non-real zeros and P is a real polynomial of degree n. Suppose thatf1 or f2 is a polynomial. It is shown that f” has at least n - 2 distinct non-real zeros. The proof is based on the iteration of transcendental meromorphic functions.

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Iteration and the zeros of the second derivative of a meromorphic function

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