On the $p$-integrality of $A$-hypergeometric series

Abstract

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.

Expanded introduction, Sections 2 and 5 rewritten, Section 7 added, small changes elsewhere

References in corpus (1)

• $A$-hypergeometric series associated to a lattice polytope with a unique interior lattice point

Cited by in corpus (4)

• On logarithmic solutions of A-hypergeometric systems
• On the integrality of factorial ratios and mirror maps
• Criterion for the integrality of hypergeometric series with parameters from quadratic fields
• On integrality properties of hypergeometric series