Abstract: For a group G, it is natural to ask how many irreducible complex representations of a given dimension it has. G is called representation rigid if, for each n, the number r_n(G) of isomorphism classes of complex irreducible ndimensional representations of G is finite. The asymptotic behaviour of the sequence {r_n(G)}_n indicates the representation growth of G; we encode r_n(G) in a Dirichlet generating series called the representation zeta function of G. In this talk, we will discuss the rationality of representation zeta functions of FAb (a property ensuring rigidity) compact p-adic analytic groups (e.g., SL_n(Z_p)) and how the model theory of valued fields plays a role in studying them with a focus on p-dependence.