MPEJ Volume 1, No.6, 24pp Received: October 5, 1995, Revised: November 30, 1995, Accepted: December 6, 1995 Hans Koch, Peter Wittwer Bounds on the Zeros of a Renormalization Group Fixed Point ABSTRACT: We prove that the Renormalization Group transformation for the Laplace transform of the d=3 Dyson-Baker hierarchical model has a nontrivial entire analytic fixed point whose zeros all lie on the imaginary axis. Sharp upper and lower bounds on 80 of these zeros are used to verify the assumptions made in reference [11]. Our proof is computer-assisted.