  By measuring the Hall coefficient R_H up to 1000 K in La_2CuO_4,
Pr_{1.3}La_{0.7}CuO_4, and La_{2-x}Sr_xCuO_4 (LSCO), we found that the
temperature (T) dependence of R_H in LSCO for x = 0 - 0.05 at high temperature
undoubtedly signifies a gap over which the charge carriers are thermally
activated, which in turn indicates that in lightly-doped cuprates strong charge
fluctuations are present at high temperature and the carrier number is not a
constant. At higher doping (x = 0.08 - 0.21), the high-temperature R_H(T)
behavior is found to be qualitatively the same, albeit with a weakened
temperature dependence, and we attempt to understand its behavior in terms of a
phenomenological two-carrier model where the thermal activation is considered
for one of the two species. Despite the crude nature of the model, our analysis
gives a reasonable account of R_H both at high temperature and at 0 K for a
wide range of doping, suggesting that charge fluctuations over a gap remain
important at high temperature in LSCO deep into the superconducting doping
regime. Moreover, our model gives a perspective to understand the seemingly
contradicting high-temperature behavior of R_H and the in-plane resistivity
near optimum doping in a consistent manner. Finally, we discuss possible
implications of our results on such issues as the scattering-time separation
and the large pseudogap.
