  Let $A$ be a set of $N$ vectors in ${\mathbb Z}^n$ and let $v$ be a vector in
${\mathbb C}^N$ that has minimal negative support for $A$. Such a vector $v$
gives rise to a formal series solution of the $A$-hypergeometric system with
parameter $\beta=Av$. If $v$ lies in ${\mathbb Q}^n$, then this series has
rational coefficients. Let $p$ be a prime number. We characterize those $v$
whose coordinates are rational, $p$-integral, and lie in the closed interval
$[-1,0]$ for which the corresponding normalized series solution has
$p$-integral coefficients. From this we deduce further integrality results for
hypergeometric series.

Number Theory