  We identify the $p$-adic unit roots of the zeta function of a projective
hypersurface over a finite field of characteristic $p$ as the eigenvalues of a
product of special values of a certain matrix of $p$-adic series. That matrix
is a product $F(\Lambda^p)^{-1}F(\Lambda)$, where the entries in the matrix
$F(\Lambda)$ are $A$-hypergeometric series with integral coefficients and
$F(\Lambda)$ is independent of $p$.
