Zeros of \(p\)-adic hypergeometric functions, \(p\)-adic analogues of Kummer's and Pfaff's identities
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Publication:2206214
DOI10.2140/PJM.2020.307.491zbMATH Open1453.11156arXiv2001.01621OpenAlexW3083224722MaRDI QIDQ2206214
Author name not available (Why is that?)
Publication date: 22 October 2020
Published in: (Search for Journal in Brave)
Abstract: We classify all the zeros and non-zero values of a family of hypergeometric series in the -adic setting. These values of hypergeometric series in the -adic setting lead to transformations of hypergeometric series in the -adic setting which can be described as -adic analogues of Kummer's and Pfaff's linear transformations on classical hypergeometric series. We also evaluate certain summation identities for hypergeometric series in the -adic setting as well as Gaussian hypergeometric series.
Full work available at URL: https://arxiv.org/abs/2001.01621
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