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 $\mathcal{Z}$ and the mean energy $<\mathcal{U}>$. 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.