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The shift of the Bose-Einstein condensation temperature for a homogenousweakly interacting Bose gas in leading order in the scattering length `a' iscomputed for given particle density `n.' Variational perturbation theory isused to resum the corresponding perturbative series for Delta<phi^2>/Nu in aclassical three-dimensional scalar field theory with coupling `u' and where thephysical case of N=2 field components is generalized to arbitrary N. Ourresults for N=1,2,4 are in agreement with recent Monte-Carlo simulations; forN=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use seven-loopperturbative coefficients, extending earlier work by one loop order.Comment: 8 pages; typos and errors of presentation fixed; beautifications;  results unchange

Bose-Einstein condensation temperature of a homogenous weakly interacting Bose gas in variational perturbation theory through seven loops