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We compute the critical temperature T_c of a weakly interacting uniform Bosegas in the canonical ensemble, extending the criterion of condensation providedby the counting statistics for the uniform ideal gas. Using ordinaryperturbation theory, we find in first order $(T_c-T_c^0)/T_c^0 = -0.93a\rho^{1/3}$, where T_c^0 is the transition temperature of the correspondingideal Bose gas, a is the scattering length, and $\rho$ is the particle numberdensity.Comment: 14 pages (RevTeX

Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble