Supercongruences for Apery-like numbers

Details Supercongruences for Apery-like numbers Supercongruences for Apery-like numbers

2009-06-18

arxiv.org/abs/0906.3413v3

Mathematics

Number Theory

8 pages, revised version, to appear in Adv. in Appl. Math

Scientific paper

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.

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