Geodesic
Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial
Mathematica Bohemica, Tome 141 (2016) no. 3, pp. 297-313
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Let $k$ be a nonnegative integer or infinity. For $a\in \mathbb {C}\cup \{\infty \}$ we denote by $E_{k}(a;f)$ the set of all $a$-points of $f$ where an $a$-point of multiplicity $m$ is counted $m$ times if $m\leq k$ and $k+1$ times if $m>k$. If $E_{k}(a;f)= E_{k}(a;g)$ then we say that $f$ and $g$ share the value $a$ with weight $k$. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).
Let $k$ be a nonnegative integer or infinity. For $a\in \mathbb {C}\cup \{\infty \}$ we denote by $E_{k}(a;f)$ the set of all $a$-points of $f$ where an $a$-point of multiplicity $m$ is counted $m$ times if $m\leq k$ and $k+1$ times if $m>k$. If $E_{k}(a;f)= E_{k}(a;g)$ then we say that $f$ and $g$ share the value $a$ with weight $k$. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).
DOI : 10.21136/MB.2016.0018-14
Classification : 30D35
Keywords: uniqueness; meromorphic function; differential polynomial; weighted sharing 
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Sahoo, Pulak. Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial. Mathematica Bohemica, Tome 141 (2016) no. 3, pp. 297-313. doi: 10.21136/MB.2016.0018-14

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