  We study properties of flux vacua in type IIB string theory in several simple
but illustrative models. We initiate the study of the relative frequencies of
vacua with vanishing superpotential W=0 and with certain discrete symmetries.
For the models we investigate we also compute the overall rate of growth of the
number of vacua as a function of the D3-brane charge associated to the fluxes,
and the distribution of vacua on the moduli space. The latter two questions can
also be addressed by the statistical theory developed by Ashok, Denef and
Douglas, and our results are in good agreement with their predictions. Analysis
of the first two questions requires methods which are more number-theoretic in
nature. We develop some elementary techniques of this type, which are based on
arithmetic properties of the periods of the compactification geometry at the
points in moduli space where the flux vacua are located.
