Supercongruences for Apery-like numbers

TL;DR

This paper establishes supercongruences for generalized Apery-like numbers, extending known congruence properties and linking them to differential equations related to zeta values.

Contribution

It introduces new supercongruences for Apery-like numbers arising from differential equations, broadening understanding of their arithmetic properties.

Findings

Proves supercongruences for generalized Apery-like numbers.

Connects these congruences to differential equations in number theory.

Extends known properties of Apery numbers to broader classes.

Abstract

It is known that the numbers which occur in Apery's proof of the irrationality of zeta(2) have many interesting congruence properties while the associated generating function satisfies a second order differential equation. We prove supercongruences for a generalization of numbers which arise in Beukers' and Zagier's study of integral solutions of Apery-like differential equations.