Date: 2022/09/18
Occasion: AMS Fall Central Sectional Meeting, Special Session on The Intersection of Number Theory and Combinatorics
Place: University of Texas at El Paso
Abstract
Apéry's proof of the irrationality of \(\zeta(3)\) relies on representing that value as the limit of the quotient of two rational solutions to a three-term recurrence. We review such Apéry limits and explore a particularly simple instance. We then explicitly determine the Apéry limits attached to sums of powers of binomial coefficients. As an application, we prove a weak version of Franel's conjecture on the order of the recurrences for these sequences. This is based on joint work with Wadim Zudilin.Download
| Link | Size | Description | Hits |
|---|---|---|---|
| 2022aperylimits-elpaso.pdf | 1.04 MB | Slides (PDF, 56 pages) | 578 |