Strong uniqueness polynomials: The complex case

Abstract

The theory of strong uniqueness polynomials, satisfying the separation condition (first introduced by Fujimoto [H. Fujimoto (2000). On uniqueness of meromorphic functions sharing finite sets. Amer. J. Math., 122, 1175–1203.]), for complex meromorphic functions is quite complete. We construct examples of strong uniqueness polynomials which do not necessary satisfy the separation condition by constructing regular 1-forms of Wronskian type, a method introduced in Ref. [T.T.H. An, J.T.-Y. Wang and P.-M. Wong. Unique range sets and uniqueness polynomials in positive characteristic. Acta Arith. (to appear).] We also use this method to produce a much easier proof in establishing the necessary and sufficient conditions for a polynomial, satisfying the separation condition, to be a strong uniqueness polynomials for meromorphic functions and rational functions.

Keywords:

• Meromorphic functions
• Uniqueness polynomials
• Wronskians
• 2000 Mathematics Subject Classifications: Primary: 12E05; Secondary: 11S80, 30D25

Notes

^†E-mail: [email protected]

*E-mail: [email protected]

*E-mail: [email protected]

Additional information

Notes on contributors

Pit-Mann Wong

†E-mail: [email protected] *E-mail: [email protected]