  A hyperplane arrangement is said to satisfy the ``Riemann hypothesis'' if all
roots of its characteristic polynomial have the same real part. This property
was conjectured by Postnikov and Stanley for certain families of arrangements
which are defined for any irreducible root system and was proved for the root
system $A_{n-1}$. The proof is based on an explicit formula for the
characteristic polynomial, which is of independent combinatorial significance.
Here our previous derivation of this formula is simplified and extended to
similar formulae for all but the exceptional root systems. The conjecture
follows in these cases.
