  We compute $2\rightarrow2$ scattering in massive $\phi^4$ theory on $\mathbb
R^{1,m}\times T^n$ to NLO. We perform the calculations using "denominator
regularization" instead of the usual dimensional regularization, which allows
for asymmetric configurations of the $T^n$. We give a transparent derivation of
and equation for the analytic continuation of the generalized Epstein zeta
function. We show that the Optical Theorem is satisfied and generalize a
conjecture by Hardy on square counting functions. We comment on the
implications.
