Uniqueness polynomials in positive characteristic

Ta Thi Hoai An
Institute of Mathematics
Academia Sinica
Nankang
Taipei 11529 Taiwan, R.O.C.
email: tthan@math.sinica.edu.tw
- Julie Tzu-Yueh Wang
Institute of Mathematics
Academia Sinica
Nankang
Taipei 11529 Taiwan, R.O.C.
email: jwang@math.sinica.edu.tw
- Pit-Mann Wong
Department of Mathematics
University of Notre Dame
Notre Dame IN 46556
U.S.A.
email: pmwong@nd.edu

Abstract:

A polynomial P is called a strong uniqueness polynomial for the family of non-constant non-archimedean entire (resp. meromorphic) functions if one cannot find two distinct non-constant non-archimedean entire (resp. meromorphic) functions f and g and a non-zero constant c such that P(f)=cP(g).

Let p>0 be the characteristic of k, n be a positive integer divided by p, and P(X) be a polynomial with P'(X) to be a constant multiple of (X-a)^m-1 where m is prime to p. We give some conditions for such polynomial P to be a strong uniqueness polynomial for non-constant non-archimedean entire (resp. meromorphic) functions.