On the value distribution of differential polynomials of meromorphic functions

Yan Xu; Huiling Qiu

Yan Xu ; Huiling Qiu

Annales Polonici Mathematici, Tome 98 (2010), p. 283-289 / Harvested from The Polish Digital Mathematics Library

Résumé

Let f be a transcendental meromorphic function of infinite order on ℂ, let k ∈ ℕ and $φ = R e^{P}$ , where R ≢ 0 is a rational function and P is a polynomial, and let $a ₀, a ₁, . . ., a_{k - 1}$ be holomorphic functions on ℂ. If all zeros of f have multiplicity at least k except possibly finitely many, and $f = 0 \Leftrightarrow f^{(k)} + a_{k - 1} f^{(k - 1)} + \dots + a ₀ f = 0$ , then $f^{(k)} + a_{k - 1} f^{(k - 1)} + \dots + a ₀ f - φ$ has infinitely many zeros.

Publié le : 2010-01-01

Zbl 1243.30074

EUDML-ID : urn:eudml:doc:280282

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Yan Xu; Huiling Qiu. On the value distribution of differential polynomials of meromorphic functions. Annales Polonici Mathematici, Tome 98 (2010) pp. 283-289. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap98-3-7/