  This article describes a sequence of rational functions which converges
locally uniformly to the zeta function. The numerators (and denominators) of
these rational functions can be expressed as characteristic polynomials of
matrices that are on the face of it very simple. As a consequence, the Riemann
hypothesis can be restated as what looks like a rather conventional spectral
problem but which is related to the one found by Connes in his analysis of the
zeta function. However the point here is that the rational approximations look
to be susceptible of quantitative estimation.
