  Using the Kirillov orbit method, novel methods from p-adic integration and
Clifford theory, we study representation zeta functions associated to compact
p-adic analytic groups. In particular, we give general estimates for the
abscissae of convergence of such zeta functions. We compute explicit formulae
for the representation zeta functions of some compact p-adic analytic groups,
defined over a compact discrete valuation ring O of characteristic 0. These
include principal congruence subgroups of SL_2(O), without any restrictions on
the residue field characteristic of O, as well as the norm one group SL_1(D) of
a non-split quaternion algebra D over the field of fractions of O and its
principal congruence subgroups. We also determine the representation zeta
functions of principal congruence subgroups of SL_3(O) in the case that O has
residue field characteristic 3 and is unramified over Z_3.
