Identity theorem for bounded p-adic meromorphic functions

International audienceLet K be a complete ultrametric algebraically closed field. We investigate several properties of sequences (a(n))(n is an element of N) in a disk d(0, R(-)) with regards to bounded analytic functions in that disk: sequences of uniqueness (when f(a(n)) = 0 for all n is an element of N implies f = 0), identity sequences (when lim(n -> + infinity) f (a(n)) = 0 implies f = 0) and analytic boundaries (when limsup(n ->infinity)vertical bar f(a(n))vertical bar = parallel to f parallel to). Particularly, we show that identity sequences and analytic boundary sequences are two equivalent properties. For certain sequences, sequences of uniqueness and identity sequences are two equivalent properties. A connection with Blaschke sequences is made. Most of the properties shown on analytic functions have continuation to meromorphic functions