Dimensional Regularization of Renyi's Statistical Mechanics

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.