Renormalization group equations and the recurrence pole relations in pure quantum gravity

In the framework of dimensional regularization, we propose a generalization renormalization group equations in case perturbative quantum gravity that involves metric and higher order Riemann curvature couplings. The zero cosmological constant is considered. Solving (RG) compute respective beta functions derive recurrence relations, valid at any Newton constant, relate pole terms 1 / ( d ? 4 ) n to single effective action. Using relations find exact form for counter-terms appear 2, 3 loops make certain statements about general structure loop. We show complete set UV divergent can be consistently (at constant) hidden bare gravitational action, includes tensor, provided couplings are renormalized according RG equations.