p-adic hypergeometric function related with p-adic multiple polylogarithms

2022/11/14 by Furusho, Hidekazu · 1 citation
#33C05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 11S80 #Secondary 12H25

paper · doi:10.48550/arxiv.2211.07155

Abstract

This paper introduces a p-adic analogue of Gauss's hypergeometric function, constructed via a method that is distinct from 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.

Cited by

• p-adic multiple zeta values and binomial multiple harmonic sums

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