  We show that the Bernstein-Sato polynomial (that is, the b-function) of a
hyperplane arrangement with a reduced equation is calculable by combining a
generalization of Malgrange's formula with the theory of Aomoto complexes due
to Esnault, Schechtman, Terao, Varchenko, and Viehweg in certain cases. We
prove in general that the roots are greater than -2 and the multiplicity of the
root -1 is equal to the (effective) dimension of the ambient space. We also
give an estimate of the multiplicities of the roots in terms of the
multiplicities of the arrangement at the dense edges, and provide a method to
calculate the Bernstein-Sato polynomial at least in the case of 3 variables
with degree at most 7 and generic multiplicities at most 3. Using our argument,
we can terminate the proof of a conjecture of Denef and Loeser on the relation
between the topological zeta function and the Bernstein-Sato polynomial of a
reduced hyperplane arrangement in the 3 variable case.
