Büchi's problem for ultrametric meromorphic functions inside an open disk

Alain Escassut (1) , Hector Pasten (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 Mathematical department

Let( $K$ be a complete ultrametric algebraically closed field of characteristic zero such as $\C_p$. Büchi's problem was solved for p-adic meromorphic functions in the whole field $K$. Here we show similar conclusions for meromorphic functions in an open disk that are not quotients of bounded analytic functions. The main method is the second Main Theorem for p-adic meromorphic functions inside a disk, a specific p-adic theorem.

Domaines: Théorie des nombres [math.NT]

Alain Escassut, Hector Pasten. Büchi's problem for ultrametric meromorphic functions inside an open disk. p-Adic Numbers, Ultrametric Analysis and Applications, 2011, 3 (2), pp.108-113. ⟨10.1134/S2070046611020038⟩. ⟨hal-00682136⟩