violating topologically massive gravity (TMG) [@Deser:1981wh] with one massive (helicity) degree of freedom, and parity even new massive gravity (NMG) [@Bergshoeff:2009hq] with two massive (helicity) degrees of freedom propagating in a unitary fashion around an anti-de Sitter (AdS) background.

Lately, one center of attention in the study of three-dimensional higher-derivative gravity were so-called logarithmic or critical tunings of the parameters. The seminal example is chiral gravity [@Li:2008dq], a fine-tuned version of TMG, which was conjectured to be dual to a logarithmic conformal field theory (LCFT) [@Grumiller:2008qz]. Besides the latter example the phenomenon of critical points was also studied in NMG, general massive gravity (GMG) [@Bergshoeff:2009hq; @Bergshoeff:2009aq] and more recently in parity even tricritical gravity (PET) [@Bergshoeff:2012ev]. For a summary on the works contributing to the LCFT conjectures in three-dimensional critical gravities see e.g. [@Bergshoeff:2012ev; @Grumiller:2010tj] and references therein.

One piece of evidence for the aforementioned critical gravity/LCFT conjecture was the calculation of one-loop partition functions on the gravity side and the results were shown to agree with those expected from a LCFT. This computation was performed for TMG and NMG in [@Gaberdiel:2010xv] and for GMG in [@Bertin:2011jk]. In this work we calculate the one-loop partition function of PET gravity along 