  Let G by compact p-adic Lie group and suppose that G is FAb, i.e., that
H/[H,H] is finite for every open subgroup H of G. The representation zeta
function Z(G,s) encodes the distribution of continuous irreducible complex
characters of G. Here s denotes a complex variable and Z(G,s) is defined as the
Dirichlet generating function whose nth coefficient is equal to the number of
irreducible characters of G of degree n. For p greater than 2 it is known that
Z(G,s) defines a meromorphic function on the complex plane.
  Wedderburn's structure theorem for semisimple algebras implies that ZG,-2) =
|G| for finite G. We complement this classic result by proving that Z(G,-2) = 0
for infinite G, assuming that p is greater than 2.
