Occasion: International conference on orthogonal polynomials and q-series
Place: University of Central Florida
AbstractThe Apéry numbers are the famous sequence which underlies Apéry's proof of the irrationality of \(\zeta(3)\). Together with their siblings, introduced by Zagier, they enjoy remarkable properties, including connections with modular forms, and have appeared in various contexts. One of their (still partially conjectural) properties is that these sequences satisfy supercongruences, a term coined by Beukers to indicate that the congruences are modulo exceptionally high powers of primes. In this talk, we introduce and discuss a \(q\)-analog of the Apéry numbers. In particular, we demonstrate that these \(q\)-analogs satisfy polynomial supercongruences.
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