Uniqueness for ultrametric analytic functions

作者：Ojeda Jacqueline^*

来源：Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, 2011, 54(2): 153-165.

• Meromorphic
• Nevanlinna
• Ultrametric
• Sharing Value
• Unicity
• Distribution of values

Let K be a complete algebraically closed p-adic field of characteristic zero and let f, g be two meromorphic functions inside an open disc of K. We first study polynomials of uniqueness for such functions. Suppose now f, g are entire functions on K. Let a is an element of K\{0} and n, k is an element of N, with k >= 2 and let a be a small entire function with respect to f and g. If f(n)(f - a)(k) f' and g(n)(g - a)(k) g' share alpha, counting multiplicities, with n >= max{6 - k,k + 1) then f = g. If alpha is an element of K* and if n >= max{5 - k, k + 1} then f = g.
Let f, g be unbounded analytic functions inside an open disk of K and let a be a small function analytic inside in the same disk. If f(n)(f - a)(2) f' and g(n)(g - a)(2)g' share alpha counting multiplicities, with n >= 4, then f = g. If f(n)(f - a)f' and g(n)(g - a)g' share alpha counting multiplicities, with n >= 5, then f = g.

• 出版日期2011