On integrality properties of hypergeometric series

Let A be a set of N vectors in Zⁿ and let v be a vector in 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 β = Av. If v lies in Qⁿ, 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.