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 Z and the mean energy 〈U〉. Renyi's entropy is characterized by a real parameter α. The poles emerge in a numerable set of rational numbers belonging to the α-line. Physical effects of these poles are studied by appeal to dimensional regularization, as usual. Interesting effects are found, as for instance, gravitational ones. In particular, negative specific heats.