p-adic hypergeometric function and p-adic multiple polylogarithms.

par Prof. Hidekazu Furusho (Université de Nagoya (Japon))

mardi 17 déc. 2024, 10:45 → 11:45 Europe/Paris

Salle Fokko du Cloux (ICJ, Université Lyon 1)

In this work, I introduce a (potentially new) p-adic analogue of the Gauss hypergeometric function, constructed using the Ohno-Zagier formula for p-adic multiple polylogarithms. I describe a method for residue-wise analytic continuation of this function and demonstrate that it satisfies a p-adic analogue of the classical Gauss hypergeometric theorem.