A short note on a pair of meromorphic functions in a p-adic field, sharing a few small ones.

A new Nevanlinna theorem on q p-adic small functions is given. Let f, g, be two meromorphic functions on a complete ultrametric algebraically closed field K of characteristic 0, or two meromorphic functions in an open disk of K , that are not quotients of bounded analytic functions by polynomials. If f and g share 7 small meromorphic functions I.M., then f = g . Better results hold when f and g satisfy some property of growth. Particularly, if f and g have finitely many poles or finitely many zeros and share 3 small meromorphic functions I.M., then f = g . [ABSTRACT FROM AUTHOR]