  The effective potentials for massless scalar and vector quantum field
theories on D dimensional manifolds with p compact noncommutative extra
dimensions are evaluated by means of dimensional regularization implemented by
zeta function techniques. It is found that the zeta function associated with
the one-loop operator may not be regular at the origin. Thus, the related
heat-kernel trace has a logarithmic term in the short t asymptotics expansion.
Consequences of this fact are briefly discussed.
