Nagoya Mathematical Journal

On uniqueness polynomials for meromorphic functions

Hirotaka Fujimoto

Abstract

A polynomial $P(w)$ is called a uniqueness polynomial (or a uiqueness polynomial in a broad sense) if $P(f) = cP(g)$ (or $P(f) = P(g)$) implies $f = g$ for any nonzero constant $c$ and nonconstant meromorphic functions $f$ and $g$ on $\mathbf C$. We consider a monic polynomial $P(w)$ without multiple zero whose derivative has mutually distinct $k$ zeros $e_j$ with multiplicities $q_j$. Under the assumption that $P(e_\ell) \not= P(e_m)$ for all distinct $\ell$ and $m$, we prove that $P(w)$ is a uniqueness polynomial in a broad sense if and only if $\sum_{\ell>m}q_\ell q_m > \sum_{\ell} q_\ell$. We also give some sufficient conditions for uniqueness polynomials.

Article information

Source
Nagoya Math. J., Volume 170 (2003), 33-46.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631875

Mathematical Reviews number (MathSciNet)
MR1994886

Zentralblatt MATH identifier
1046.30011

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory

Citation

Fujimoto, Hirotaka. On uniqueness polynomials for meromorphic functions. Nagoya Math. J. 170 (2003), 33--46. https://projecteuclid.org/euclid.nmj/1114631875

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