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On uniqueness polynomials for meromorphic functions

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa, 920-1192, Japan, [email protected]
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Abstract

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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 C. We consider a monic polynomial P(w) without multiple zero whose derivative has mutually distinct k zeros ej with multiplicities qj. Under the assumption that P(el) ≠ P(em) for all distinct l and m, we prove that P(w) is a uniqueness polynomial in a broad sense if and only if ∑l<mqlqm > ∑l ql. We also give some sufficient conditions for uniqueness polynomials.

Keywords

30D35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 170 , 2003 , pp. 33 - 46
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

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