Iteration and the Zeros of the Second Derivative of a Meromorphic Function

Hinkkanen, A.

doi:10.1112/plms/s3-65.3.629

Cited by 16 publications

(14 citation statements)

References 11 publications

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“…[108, §7]). Hinkkanen [83,Theorem 2] has shown that in certain cases this argument may also be used to prove that Baker domains contain singularities of f −1 . We note that the conclusion of Corollary 3 does not hold in general for f ∈ M ∩B.…”

Section: Julia's Approachmentioning

confidence: 99%

Iteration of meromorphic functions

Bergweiler¹

1993

Bull. Amer. Math. Soc.

530

577

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Section: Julia's Approachmentioning

confidence: 99%

Iteration of meromorphic functions

Bergweiler¹

1993

Bull. Amer. Math. Soc.

530

577

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“…To demonstrate how dynamics works we begin with a simple direct proof of Corollary 1.1 found by the second author in 1989 after reading Sheil-Small's paper. This dynamical proof is also reproduced in [8].…”

Section: 3])mentioning

confidence: 59%

Zeros of Differential Polynomials in Real Meromorphic Functions

Bergweiler¹,

Erëmenko²,

Langley³

2005

Proceedings of the Edinburgh Mathematical Society

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We investigate whether differential polynomials in real transcendental meromorphic functions have non-real zeros. For example, we show that if g is a real transcendental meromorphic function, c ∈ R \ {0} and n 3 is an integer, then g g n − c has infinitely many non-real zeros. If g has only finitely many poles, then this holds for n 2. Related results for rational functions g are also considered.

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“…In [95] the same authors with Shen classified all entire functions (not necessarily real) with the property that f f f has only real zeros. The classification of meromorphic functions with the property that all their derivatives have only real zeros was achieved by Hinkkanen [86,87,88,89,90].…”

Section: Chapter VImentioning

confidence: 99%

A survey of some results after 1970

2008

Translations of Mathematical Monographs

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The literature on meromorphic functions 1 is very large. There is a comprehensive survey [62] that contains everything that was reviewed on the topic in the Soviet "Referativnyi Zhurnal" in 1953-1970, and a later large survey [67]. More recent surveys [30], [80] and [48] are shorter and have narrower scope. Some books on specific topics in the theory of meromorphic functions published after 1970 are [18], [20], [79], [100], [137], [134], [138], [162]. A survey of the fast developing subject of iteration of meromorphic functions is [7]. Here we give a short survey of some results which are closely related to the problems considered in this book. Thus we do not include many important topics, like geometric theory of meromorphic functions, iteration, composition, differential and functional equations, normal families, Borel and Julia directions, uniqueness theorems, and most regrettably, holomorphic curves and quasiregular mappings.

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Iteration and the Zeros of the Second Derivative of a Meromorphic Function

Cited by 16 publications

References 11 publications

Iteration of meromorphic functions

Iteration of meromorphic functions

Zeros of Differential Polynomials in Real Meromorphic Functions

A survey of some results after 1970

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