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p-Adic Hypergeometric Function Related with p-Adic Multiple Polylogarithms
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DOI：10.1007/s00025-026-02666-9.png)
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Abstract
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This paper introduces a p-adic analogue of Gauss's hypergeometric function, constructed via a method that is distinct from Dwork's approach. The idea of our construction is motivated by the Ohno-Zagier formula, which is elucidated through the relationship between the hypergeometric differential equation and the Knizhnik-Zamolodchikov (KZ) equation. We develop a rigorous framework for the residue-wise analytic prolongation of our p-adic hypergeometric function by exploring its relationship with p-adic multiple polylogarithms. Through a detailed analysis of its local behavior near the point 1, we show a p-adic version of Gauss hypergeometric theorem for the function.
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