  We study the representation growth of simple compact Lie groups and of
$\mathrm{SL}_n(\mathcal{O})$, where $\mathcal{O}$ is a compact discrete
valuation ring, as well as the twist representation growth of
$\mathrm{GL}_n(\mathcal{O})$. This amounts to a study of the abscissae of
convergence of the corresponding (twist) representation zeta functions.
  We determine the abscissae for a class of Mellin zeta functions which include
the Witten zeta functions. As a special case, we obtain a new proof of the
theorem of Larsen and Lubotzky that the abscissa of Witten zeta functions is
$r/\kappa$, where $r$ is the rank and $\kappa$ the number of positive roots.
  We then show that the twist zeta function of $\mathrm{GL}_n(\mathcal{O})$
exists and has the same abscissa of convergence as the zeta function of
$\mathrm{SL}_n(\mathcal{O})$, provided $n$ does not divide
$\text{char}\,{\mathcal{O}}$. We compute the twist zeta function of
$\mathrm{GL}_2(\mathcal{O})$ when the residue characteristic $p$ of
$\mathcal{O}$ is odd, and approximate the zeta function when $p=2$ to deduce
that the abscissa is $1$. Finally, we construct a large part of the
representations of $\mathrm{SL}_2(\mathbb{F}_q[[t]])$, $q$ even, and deduce
that its abscissa lies in the interval $[1,\,5/2]$.
