  Dirac spectrum representations of the Polyakov loop fluctuations are derived
on the temporally odd-number lattice, where the temporal length is odd with the
periodic boundary condition. We investigate the Polyakov loop fluctuations
based on these analytical relations. It is semianalytically and numerically
found that the low-lying Dirac eigenmodes have little contribution to the
Polyakov loop fluctuations, which are sensitive probe for the quark
deconfinement. Our results suggest no direct one-to-one corresponding between
quark confinement and chiral symmetry breaking in QCD.
