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Talk: Supercongruences for Apéry-like numbers (AKLS)

Supercongruences for Apéry-like numbers (AKLS)

Date: 2015/03/11
Occasion: Seminar Aachen-Köln-Lille-Siegen on Automorphic Forms
Place: Universität zu Köln

Abstract

Apéry-like numbers are special integer sequences, going back to Beukers and Zagier, which are modeled after and share many of the properties of the numbers that underlie Apéry's proof of the irrationality of $$\zeta(3)$$. Among their remarkable properties are connections with modular forms and so-called supercongruences of various types, some of which remain conjectural. We discuss these congruences and report on recent generalizations, including a polynomial analog. This talk includes joint work with Robert Osburn and Brundaban Sahu.