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arXiv · 1905.03235

On integrality properties of hypergeometric series

Alan Adolphson·Steven Sperber
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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. From this we deduce further integrality results for hypergeometric series.

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Alan Adolphson, Steven Sperber. 2019-05-08. On integrality properties of hypergeometric series. https://arxiv.org/abs/1905.03235

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