**Sums of powers of binomials, their Apéry limits, and Franel's suspicions (LSU)**

**Date:** 2022/03/13
**Occasion:** Southern Regional Number Theory Conference
**Place:** Louisiana State University

## 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 |
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2022aperylimits-lsu.pdf | 1.38 MB | Slides (PDF, 123 pages) | 622 |