arminstraub.com

Talk: Sums of powers of binomials, their Apéry limits, and Franel's suspicions (El Paso)

Sums of powers of binomials, their Apéry limits, and Franel's suspicions (El Paso)

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

LinkSizeDescriptionHits
1.04 MB Slides (PDF, 56 pages) 33