Derivatives of meromorphic functions with multiple zeros and elliptic functions

Pai Yang; Shahar Nevo

doi:10.1007/s10114-013-2375-x

Derivatives of meromorphic functions with multiple zeros and elliptic functions

Pai Yang, Shahar Nevo

Department of Mathematics

Bar-Ilan University

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

Abstract

Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple except finitely many and T(r, h) = o{T(r, f)} as r→∞, then f′ = h has infinitely many solutions (including poles).

Original language	English
Pages (from-to)	1257-1278
Number of pages	22
Journal	Acta Mathematica Sinica, English Series
Volume	29
Issue number	7
DOIs	https://doi.org/10.1007/s10114-013-2375-x
State	Published - Jul 2013

Keywords

Normal family
elliptic function

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1007/s10114-013-2375-x

Cite this

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abstract = "Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple except finitely many and T(r, h) = o{T(r, f)} as r→∞, then f′ = h has infinitely many solutions (including poles).",

keywords = "Normal family, elliptic function",

author = "Pai Yang and Shahar Nevo",

note = "Funding Information: Received June 19, 2012, accepted October 19, 2012 The second author is supported by the Israel Science Foundation (Grant No. 395/2007)",

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AU - Nevo, Shahar

N1 - Funding Information: Received June 19, 2012, accepted October 19, 2012 The second author is supported by the Israel Science Foundation (Grant No. 395/2007)

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N2 - Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple except finitely many and T(r, h) = o{T(r, f)} as r→∞, then f′ = h has infinitely many solutions (including poles).

AB - Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple except finitely many and T(r, h) = o{T(r, f)} as r→∞, then f′ = h has infinitely many solutions (including poles).

KW - Normal family

KW - elliptic function

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DO - 10.1007/s10114-013-2375-x

M3 - مقالة

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VL - 29

SP - 1257

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

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ER -

Derivatives of meromorphic functions with multiple zeros and elliptic functions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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