Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 36, 2011, 47-70

DIFFERENTIAL POLYNOMIALS AND SHARED VALUES

Jürgen Grahl and Shahar Nevo

University of Würzburg, Department of Mathematics
Am Hubland, 97074 Würzburg, Germany; grahl 'at' mathematik.uni-wuerzburg.de

Bar-Ilan University, Department of Mathematics
Ramat-Gan 52900, Israel; nevosh 'at' macs.biu.ac.il

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 \ge 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.

2000 Mathematics Subject Classification: Primary 30D35.

Key words: Shared values, differential polynomials, uniqueness of meromorphic functions.

Reference to this article: J. Grahl and S. Nevo: Differential polynomials and shared values. Ann. Acad. Sci. Fenn. Math. 36 (2011), 47-70.

Full document as PDF file

doi:10.5186/aasfm.2011.3603

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