Zeros of the Gell-Mann-Low function and Borel summations in renormalizable theories

A Borel type summation of perturbation series with a conformal map of the Borel variable is considered for the case where renormalon singularities are present. Application of this method to lambdaphi4/4factorial field theory in four dimensions allows one to compute a sum for the Gell-Mann-Low function, β(lambda), for 0 < (lambda/16π2) < 0.7. This sum has an ultraviolet stable zero of β at (lambda/16π2) = 0.41. The case of quantum electrodynamics is also briefly considered. (Auth.)