Rationality of twist representation zeta functions of compact p-adic analytic groups

We prove that for any twist rigid compact p-adic analytic group G, its twist representation zeta function is a finite sum of terms n −s i f i (p −s), where n i are natural numbers and f i (t) ∈ Q(t) are rational functions. Mero-morphic continuation and rationality of the abscissa of the zeta function follow as corollaries. If G is moreover a prop group, we prove that its twist representation zeta function is rational in p −s. To establish these results we develop a Clifford theory for twist isoclasses of representations, including a new coho-mological invariant of a twist isoclass.