Date: 2025/10/09
Occasion: Quebec-Vermont Number Theory Seminar
Place: Montréal
Abstract
Apéry-like numbers are special integer sequences, going back to Beukers and Zagier, which are modelled after and share many of the properties of the numbers that underlie Apéry's proof of the irrationality of \(\zeta(3)\). They exhibit remarkable arithmetic properties, including connections with modular forms and unusually strong congruences. We survey these and report on new perspectives and recent progress. In particular, we illustrate how Aperéry-like numbers feature in various, apparently unrelated, problems. The examples are taken from personal research of the speaker and include the theories of short random walks, series for \(1/\pi\), and positivity of rational functions. Throughout, numerous open problems will be advertised.Download
| Link | Size | Description | Hits |
|---|---|---|---|
| 2025aperyubiquity-montreal.pdf | 3.72 MB | Slides (PDF, 283 pages) | 64 |