  A theory of the static electron polarizability of crystals whose energy
spectrum is modified by quantizing magnetic fields is presented. It is argued
that The polarizability is strongly affected by non-dissipative Hall currents
induced by the presence of crossed electric and magnetic fields: these can even
change its sign. Results are illustrated in detail for a two dimensional square
lattice. The polarizability and the Hall conductivity are respectively linked
to the two topological quantum numbers entering the so--called Diophantine
equation. These numbers could in principle be detected in actual experiments.
