Seminar talk: “Sums of powers of binomials, their Apery limits, and Franel’s suspicions” (Speaker: Prof. Armin Straub, University of South Alabama)

Description

Ap\'ery'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 Ap\'ery limits and explore a particularly simple instance. We then explicitly determine the Ap\'ery 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.

Period	27 Apr 2022
Event type	Guest talk
Location	AustriaShow on map