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2002•International Journal of MathematicsRequires access

UNIQUENESS POLYNOMIALS FOR COMPLEX MEROMORPHIC FUNCTIONS

Ta Thi Hoai An, Julie Tzu‐Yueh Wang

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Abstract

A polynomial P(X) in [Formula: see text] is called a strong uniqueness polynomial for meromorphic functions if whenever there exist two non-constant meromorphic functions f and g and a complex non-zero constant c such that P(f) = cP(g), then we must have f = g. In this paper, we give a necessary and sufficient condition for a polynomial to be a strong uniqueness polynomial for meromorphic functions under the assumption that P(X) is injective on the roots of P′(X) = 0.

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What this paper is about

A polynomial P(X) in [Formula: see text] is called a strong uniqueness polynomial for meromorphic functions if whenever there exist two non-constant meromorphic functions f and g and a complex non-zero constant c such that P(f) = cP(g), then we must have f = g. In this paper, we give a necessary and sufficient condition for a polynomial to be a strong uniqueness polynomial for meromorphic functions under the assumption that P(X) is injective on the roots of P′(X) = 0.

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Available abstract

A polynomial P(X) in [Formula: see text] is called a strong uniqueness polynomial for meromorphic functions if whenever there exist two non-constant meromorphic functions f and g and a complex non-zero constant c such that P(f) = cP(g), then we must have f = g. In this paper, we give a necessary and sufficient condition for a polynomial to be a strong uniqueness polynomial for meromorphic functions under the assumption that P(X) is injective on the roots of P′(X) = 0.

Key concepts: Meromorphic function, Uniqueness, Mathematics, Injective function, Polynomial, Constant (computer programming), Zero (linguistics), Pure mathematics

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