One-loop effective potential for scalar and vector fields on higher   dimensional noncommutative flat manifolds
  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. 
A.A Bytsenko, A.E. Goncalves and S. Zerbini