Congruence relations for $p$-adic hypergeometric functions ${\hat{\mathcal{F}}}_{a,...,a}^{(\sigma )}(t)$ and its transformation formula

Abstract

We introduce new kind of $p$-adic hypergeometric functions. We show these functions satisfy congruence relations, so they are convergent functions. And we show that there is a transformation formula between our new $p$-adic hypergeometric functions and $p$-adic hypergeometric functions of logarithmic type defined by M. Asakura in a particular case.

39 pages

References in corpus (1)

• New p-adic hypergeometric functions and syntomic regulators