  Let $R$ be an $E_\infty$-ring spectrum. Given a map $\zeta$ from a space $X$
to $BGL_1R$, one can construct a Thom spectrum, $X^\zeta$, which generalises
the classical notion of Thom spectrum for spherical fibrations in the case
$R=S^0$, the sphere spectrum. If $X$ is a loop space ($\simeq \Omega Y$) and
$\zeta$ is homotopy equivalent to $\Omega f$ for a map $f$ from $Y$ to
$B^2GL_1R$, then the Thom spectrum has an $A_\infty$-ring structure. The
Topological Hochschild Homology of these $A_\infty$-ring spectra is equivalent
to the Thom spectrum of a map out of the free loop space of $Y$.
  This paper considers the case $X=S^1$, $R=K_p^\wedge$, the p-adic $K$-theory
spectrum, and $\zeta = 1-p \in \pi_1BGL_1K_p^\wedge$. The associated Thom
spectrum $(S^1)^\zeta$ is equivalent to the mod p $K$-theory spectrum $K/p$.
The map $\zeta$ is homotopy equivalent to a loop map, so the Thom spectrum has
an $A_\infty$-ring structure. I will compute $\pi_*THH^{K_p^\wedge}(K/p)$ using
its description as a Thom spectrum.
