  The non-equilibrium dynamics of the kinetic spherical model, quenched to
T<=T_c, with a non-conserved order-parameter is studied at its upper critical
dimension d=d*=4. In the scaling limit where both the waiting time s and the
observation time t are large and the ratio y=t/s>1 is fixed, the scaling
functions of the two-time autocorrelation and autoresponse functions do not
contain any logarithmic correction factors and the typical size of correlated
domains scales for large times as L(t) ~ t^0.5 .
