Meromorphic functions on annuli sharing finite sets with truncated multiplicity
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Publication:6391560
DOI10.1016/J.JMAA.2022.126872arXiv2202.09523MaRDI QIDQ6391560
Publication date: 18 February 2022
Abstract: The purpose of this paper has twofold. The first is to establish a second main theorem for meromorphic functions on annuli and meromorphic function targets (may not be small functions) with truncated counting functions (truncation level 1) and with a detailed estimate for the error term. The second is to show that if the polynomial $$P_S(w)=(w-a_1)cdots (w-a_q)$$ is a uniqueness polynomial for admissible meromorphic functions on an annulus $mathbb A(R_0)$ such that $P'_S(w)$ has exactly $k$ distinct zeros and $q>frac{(5k+7)ell}{2ell-175}$, then the set $S={a_1,ldots,a_q}$ is a finite range set with truncation level $ell$ for admissible meromorphic functions on $mathbb A(R_0)$. This result extends the previous result on the finite range set (with truncation level $ell=infty$) for holomorphic functions on $mathbb C$ of H. Fujimoto.
Arithmetic problems in algebraic geometry; Diophantine geometry (14Gxx) Entire and meromorphic functions of one complex variable, and related topics (30Dxx) Two-dimensional potential theory (31Axx)
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