Differential polynomials and shared values

Jürgen Grahl; Shahar Nevo

doi:10.5186/aasfm.2011.3603

Differential polynomials and shared values

Jürgen Grahl
, Shahar Nevo

Department of Mathematics

University of Würzburg

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

5 Scopus citations

Abstract

Let f and g be non-constant meromorphic functions in C, a and b non-zero complex numbers and let n and k be natural numbers satisfying n ≥ 5k + 17. We show that if the differential polynomials fⁿ + af^(k) and gⁿ + ag^(k) share the value b CM, then f and g are either equal or at least closely related.

Original language	English
Pages (from-to)	47-70
Number of pages	24
Journal	Annales Academiae Scientiarum Fennicae Mathematica
Volume	36
Issue number	1
DOIs	https://doi.org/10.5186/aasfm.2011.3603
State	Published - 2011

Keywords

Differential polynomials
Shared values
Uniqueness of meromorphic functions

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10.5186/aasfm.2011.3603

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abstract = "Let f and g be non-constant meromorphic functions in C, a and b non-zero complex numbers and let n and k be natural numbers satisfying n ≥ 5k + 17. We show that if the differential polynomials fn + af(k) and gn + ag(k) share the value b CM, then f and g are either equal or at least closely related.",

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AU - Nevo, Shahar

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AB - Let f and g be non-constant meromorphic functions in C, a and b non-zero complex numbers and let n and k be natural numbers satisfying n ≥ 5k + 17. We show that if the differential polynomials fn + af(k) and gn + ag(k) share the value b CM, then f and g are either equal or at least closely related.

KW - Differential polynomials

KW - Shared values

KW - Uniqueness of meromorphic functions

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JF - Annales Academiae Scientiarum Fennicae Mathematica

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Differential polynomials and shared values

Abstract

Keywords

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