Open Access
2009 On a result of H. Fujimoto
Xiaotian Bai, Qi Han, Ang Chen
J. Math. Kyoto Univ. 49(3): 631-643 (2009). DOI: 10.1215/kjm/1260975043


Let $P(\omega)$ be a uniqueness polynomial of degree $q$ without multiple zeros whose derivative has mutually distinct $k$ zeros $d_l$ with multiplicities $q_l$ for $l=1, 2, \ldots, k$ respectively, and let $S:=\{a_1, a_2, \cdots, a_q\}$ be the zero set of $P(\omega)$. Under the assumption that $P(d_{l_s})\neq P(d_{l_t})$ $(1\leq l_s < l_t\leq k)$, we give some sufficient conditions for the set $S$ to be a unique range set with some weak value-sharing hypothesis, namely, to satisfy the condition that $\sum_{j=1}^q\nu_{f,m_0)}^{a_j}\equiv\sum_{j=1}^q\nu_{g,m_0)}^{a_j}$ ($m_0\in\mathbb{Z}^+\cup\{\infty\}$) implies $f\equiv g$ for any two nonconstant meromorphic or entire functions $f$ and $g$ on $\mathbb{C}$, which improve a result of H. Fujimoto. Also, we discuss some other related topics.


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Xiaotian Bai. Qi Han. Ang Chen. "On a result of H. Fujimoto." J. Math. Kyoto Univ. 49 (3) 631 - 643, 2009.


Published: 2009
First available in Project Euclid: 16 December 2009

zbMATH: 1193.30035
MathSciNet: MR2583606
Digital Object Identifier: 10.1215/kjm/1260975043

Primary: 30D20 , 30D35

Rights: Copyright © 2009 Kyoto University

Vol.49 • No. 3 • 2009
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