  We show that typical Renyi's statistical mechanics' quantifiers exhibit
poles. We are referring to the partition function ${\cal Z}$ and the mean
energy $<{\cal U}>$. Renyi's entropy is characterized by a real parameter
$\alpha$. The poles emerge in a numerable set of rational numbers belonging to
the $\alpha-$line. Physical effects of these poles are studied by appeal to
dimensional regularization, as usual. Interesting effects are found, as for
instance, gravitational ones.
