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# Talk: On the ubiquity of modular forms and Apéry-like numbers (Dublin)

On the ubiquity of modular forms and Apéry-like numbers (Dublin)

Date: 2013/11/18
Occasion: Algebra and Number Theory Seminar
Place: University College Dublin

## Abstract

Apéry-like numbers are special sequences which are modelled after and share many of the properties of the numbers that underlie Apéry's proof of the irrationality of $$\zeta(3)$$. In the course of several examples, we demonstrate how these numbers and their connection with modular forms feature in various, apparently unrelated, problems. The examples are taken from personal research of the speaker and include the theories of short random walks, binomial congruences, positivity of rational functions and series for $$1/\pi$$.