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September 2021 On integrality properties of hypergeometric series
Adolphson Alan, Sperber Steven
Funct. Approx. Comment. Math. 65(1): 7-31 (September 2021). DOI: 10.7169/facm/1843

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.

Citation

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Adolphson Alan. Sperber Steven. "On integrality properties of hypergeometric series." Funct. Approx. Comment. Math. 65 (1) 7 - 31, September 2021. https://doi.org/10.7169/facm/1843

Information

Published: September 2021
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.7169/facm/1843

Subjects:
Primary: 11Z05, 14G99, 33C70

Rights: Copyright © 2021 Adam Mickiewicz University

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Vol.65 • No. 1 • September 2021
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