P-adic hypergeometrics

TL;DR

This paper explores the properties of classical hypergeometric series within the p-adic number framework, inspired by a problem discussed by D. Zagier, aiming to deepen understanding of hypergeometric functions in p-adic analysis.

Contribution

It introduces a novel perspective on hypergeometric series as p-adic functions, extending classical analysis into the p-adic domain inspired by Zagier's problem.

Findings

Hypergeometric series can be viewed as p-adic functions.

New insights into p-adic properties of hypergeometric series.

Connections between hypergeometric motives and p-adic analysis.

Abstract

We study classical hypergeometric series as a p-adic function of its parameters inspired by a problem in the American Mathematical Monthly solved by D. Zagier. This is an extended abstract of a talk given at the workshop "Hypergeometric motives and Calabi-Yau differential equations" at the Mathematical Research Institute (MATRIX) of The University of Melbourne in Creswick, Australia in January of 2017.